id int64 1 14M | domain stringclasses 6
values | topic stringclasses 23
values | subtopic stringclasses 37
values | difficulty int64 1 8 | unit_type stringclasses 3
values | title stringlengths 14 86 | content stringlengths 203 553 | key_equations stringclasses 23
values | prerequisites stringclasses 29
values | learning_objective stringclasses 37
values |
|---|---|---|---|---|---|---|---|---|---|---|
701 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5915 Hz, speed 1038 m/s | A periodic wave travels at speed v = 1038 m/s with frequency f = 5915 Hz. The wavelength is λ = v / f = 0.1754 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
702 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 4398 Hz, speed 460.3 m/s | A periodic wave travels at speed v = 460.3 m/s with frequency f = 4398 Hz. The wavelength is λ = v / f = 0.1047 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
703 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3081 Hz, speed 1197 m/s | A periodic wave travels at speed v = 1197 m/s with frequency f = 3081 Hz. The wavelength is λ = v / f = 0.3886 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
704 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.2123e+04 Hz, speed 799 m/s | A periodic wave travels at speed v = 799 m/s with frequency f = 1.2123e+04 Hz. The wavelength is λ = v / f = 0.06591 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
705 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0994e+04 Hz, speed 865 m/s | A periodic wave travels at speed v = 865 m/s with frequency f = 1.0994e+04 Hz. The wavelength is λ = v / f = 0.07868 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
706 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0760e+04 Hz, speed 1097 m/s | A periodic wave travels at speed v = 1097 m/s with frequency f = 1.0760e+04 Hz. The wavelength is λ = v / f = 0.1019 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
707 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 4384 Hz, speed 597 m/s | A periodic wave travels at speed v = 597 m/s with frequency f = 4384 Hz. The wavelength is λ = v / f = 0.1362 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
708 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.5100e+04 Hz, speed 1348 m/s | A periodic wave travels at speed v = 1348 m/s with frequency f = 1.5100e+04 Hz. The wavelength is λ = v / f = 0.08926 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
709 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1656 Hz, speed 836.1 m/s | A periodic wave travels at speed v = 836.1 m/s with frequency f = 1656 Hz. The wavelength is λ = v / f = 0.505 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
710 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4081e+04 Hz, speed 393.7 m/s | A periodic wave travels at speed v = 393.7 m/s with frequency f = 1.4081e+04 Hz. The wavelength is λ = v / f = 0.02796 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
711 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1292e+04 Hz, speed 374.1 m/s | A periodic wave travels at speed v = 374.1 m/s with frequency f = 1.1292e+04 Hz. The wavelength is λ = v / f = 0.03313 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
712 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0962e+04 Hz, speed 906.6 m/s | A periodic wave travels at speed v = 906.6 m/s with frequency f = 1.0962e+04 Hz. The wavelength is λ = v / f = 0.0827 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
713 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1463e+04 Hz, speed 479.8 m/s | A periodic wave travels at speed v = 479.8 m/s with frequency f = 1.1463e+04 Hz. The wavelength is λ = v / f = 0.04186 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
714 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 6576 Hz, speed 924.4 m/s | A periodic wave travels at speed v = 924.4 m/s with frequency f = 6576 Hz. The wavelength is λ = v / f = 0.1406 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
715 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 2342 Hz, speed 546.5 m/s | A periodic wave travels at speed v = 546.5 m/s with frequency f = 2342 Hz. The wavelength is λ = v / f = 0.2333 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
716 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 957.9 J, W = -654.5 J | A thermodynamic system exchanges heat Q = 957.9 J with its surroundings and performs work W = -654.5 J. By the first law, the change in internal energy is ΔU = Q − W = 1612 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
717 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 775.9 J, W = 493.9 J | A thermodynamic system exchanges heat Q = 775.9 J with its surroundings and performs work W = 493.9 J. By the first law, the change in internal energy is ΔU = Q − W = 282 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
718 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 633.6 J, W = 21.2 J | A thermodynamic system exchanges heat Q = 633.6 J with its surroundings and performs work W = 21.2 J. By the first law, the change in internal energy is ΔU = Q − W = 612.4 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
719 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 642 J, W = -707.6 J | A thermodynamic system exchanges heat Q = 642 J with its surroundings and performs work W = -707.6 J. By the first law, the change in internal energy is ΔU = Q − W = 1350 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
720 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 655.9 J, W = 491.1 J | A thermodynamic system exchanges heat Q = 655.9 J with its surroundings and performs work W = 491.1 J. By the first law, the change in internal energy is ΔU = Q − W = 164.9 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
721 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1308 J, W = -166.5 J | A thermodynamic system exchanges heat Q = 1308 J with its surroundings and performs work W = -166.5 J. By the first law, the change in internal energy is ΔU = Q − W = 1475 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
722 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1541 J, W = 393.3 J | A thermodynamic system exchanges heat Q = 1541 J with its surroundings and performs work W = 393.3 J. By the first law, the change in internal energy is ΔU = Q − W = 1148 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
723 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 945.8 J, W = -727.5 J | A thermodynamic system exchanges heat Q = 945.8 J with its surroundings and performs work W = -727.5 J. By the first law, the change in internal energy is ΔU = Q − W = 1673 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
724 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 361.3 J, W = -698 J | A thermodynamic system exchanges heat Q = 361.3 J with its surroundings and performs work W = -698 J. By the first law, the change in internal energy is ΔU = Q − W = 1059 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
725 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1985 J, W = 695.3 J | A thermodynamic system exchanges heat Q = 1985 J with its surroundings and performs work W = 695.3 J. By the first law, the change in internal energy is ΔU = Q − W = 1290 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
726 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -327.5 J, W = 694 J | A thermodynamic system exchanges heat Q = -327.5 J with its surroundings and performs work W = 694 J. By the first law, the change in internal energy is ΔU = Q − W = -1021 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
727 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -420.7 J, W = -145.8 J | A thermodynamic system exchanges heat Q = -420.7 J with its surroundings and performs work W = -145.8 J. By the first law, the change in internal energy is ΔU = Q − W = -274.8 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
728 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1422 J, W = 425.3 J | A thermodynamic system exchanges heat Q = 1422 J with its surroundings and performs work W = 425.3 J. By the first law, the change in internal energy is ΔU = Q − W = 997.1 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
729 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1946 J, W = 233.4 J | A thermodynamic system exchanges heat Q = 1946 J with its surroundings and performs work W = 233.4 J. By the first law, the change in internal energy is ΔU = Q − W = 1712 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
730 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 550.9 J, W = 788.6 J | A thermodynamic system exchanges heat Q = 550.9 J with its surroundings and performs work W = 788.6 J. By the first law, the change in internal energy is ΔU = Q − W = -237.7 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
731 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 456.2 J, W = 591.4 J | A thermodynamic system exchanges heat Q = 456.2 J with its surroundings and performs work W = 591.4 J. By the first law, the change in internal energy is ΔU = Q − W = -135.2 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
732 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1767 J, W = -199 J | A thermodynamic system exchanges heat Q = 1767 J with its surroundings and performs work W = -199 J. By the first law, the change in internal energy is ΔU = Q − W = 1966 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
733 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1207 J, W = 258.9 J | A thermodynamic system exchanges heat Q = 1207 J with its surroundings and performs work W = 258.9 J. By the first law, the change in internal energy is ΔU = Q − W = 948 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
734 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 848.3 J, W = 245.7 J | A thermodynamic system exchanges heat Q = 848.3 J with its surroundings and performs work W = 245.7 J. By the first law, the change in internal energy is ΔU = Q − W = 602.6 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
735 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 369.4 J, W = -514.4 J | A thermodynamic system exchanges heat Q = 369.4 J with its surroundings and performs work W = -514.4 J. By the first law, the change in internal energy is ΔU = Q − W = 883.9 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
736 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 843.1 J, W = 46.15 J | A thermodynamic system exchanges heat Q = 843.1 J with its surroundings and performs work W = 46.15 J. By the first law, the change in internal energy is ΔU = Q − W = 797 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
737 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1320 J, W = -443.7 J | A thermodynamic system exchanges heat Q = 1320 J with its surroundings and performs work W = -443.7 J. By the first law, the change in internal energy is ΔU = Q − W = 1763 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
738 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -491.3 J, W = -763.6 J | A thermodynamic system exchanges heat Q = -491.3 J with its surroundings and performs work W = -763.6 J. By the first law, the change in internal energy is ΔU = Q − W = 272.3 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
739 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 245.9 J, W = 277.6 J | A thermodynamic system exchanges heat Q = 245.9 J with its surroundings and performs work W = 277.6 J. By the first law, the change in internal energy is ΔU = Q − W = -31.69 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
740 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 861.1 J, W = 51.09 J | A thermodynamic system exchanges heat Q = 861.1 J with its surroundings and performs work W = 51.09 J. By the first law, the change in internal energy is ΔU = Q − W = 810 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
741 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1558 J, W = -404 J | A thermodynamic system exchanges heat Q = 1558 J with its surroundings and performs work W = -404 J. By the first law, the change in internal energy is ΔU = Q − W = 1962 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
742 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 365.4 J, W = -359 J | A thermodynamic system exchanges heat Q = 365.4 J with its surroundings and performs work W = -359 J. By the first law, the change in internal energy is ΔU = Q − W = 724.4 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
743 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1844 J, W = 360 J | A thermodynamic system exchanges heat Q = 1844 J with its surroundings and performs work W = 360 J. By the first law, the change in internal energy is ΔU = Q − W = 1483 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
744 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -217.9 J, W = 495.2 J | A thermodynamic system exchanges heat Q = -217.9 J with its surroundings and performs work W = 495.2 J. By the first law, the change in internal energy is ΔU = Q − W = -713.1 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
745 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 548.1 J, W = 425.7 J | A thermodynamic system exchanges heat Q = 548.1 J with its surroundings and performs work W = 425.7 J. By the first law, the change in internal energy is ΔU = Q − W = 122.4 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
746 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1709 J, W = -775 J | A thermodynamic system exchanges heat Q = 1709 J with its surroundings and performs work W = -775 J. By the first law, the change in internal energy is ΔU = Q − W = 2484 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
747 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 15.2 J, W = -638.6 J | A thermodynamic system exchanges heat Q = 15.2 J with its surroundings and performs work W = -638.6 J. By the first law, the change in internal energy is ΔU = Q − W = 653.8 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
748 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -416.1 J, W = 156.5 J | A thermodynamic system exchanges heat Q = -416.1 J with its surroundings and performs work W = 156.5 J. By the first law, the change in internal energy is ΔU = Q − W = -572.5 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
749 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1258 J, W = -722.1 J | A thermodynamic system exchanges heat Q = 1258 J with its surroundings and performs work W = -722.1 J. By the first law, the change in internal energy is ΔU = Q − W = 1980 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
750 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1351 J, W = -156.4 J | A thermodynamic system exchanges heat Q = 1351 J with its surroundings and performs work W = -156.4 J. By the first law, the change in internal energy is ΔU = Q − W = 1508 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
751 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 85.85 J, W = -452.4 J | A thermodynamic system exchanges heat Q = 85.85 J with its surroundings and performs work W = -452.4 J. By the first law, the change in internal energy is ΔU = Q − W = 538.2 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
752 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1659 J, W = -709.7 J | A thermodynamic system exchanges heat Q = 1659 J with its surroundings and performs work W = -709.7 J. By the first law, the change in internal energy is ΔU = Q − W = 2369 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
753 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 759.7 J, W = -337.2 J | A thermodynamic system exchanges heat Q = 759.7 J with its surroundings and performs work W = -337.2 J. By the first law, the change in internal energy is ΔU = Q − W = 1097 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
754 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1539 J, W = 370.4 J | A thermodynamic system exchanges heat Q = 1539 J with its surroundings and performs work W = 370.4 J. By the first law, the change in internal energy is ΔU = Q − W = 1169 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
755 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 297.3 J, W = 156.7 J | A thermodynamic system exchanges heat Q = 297.3 J with its surroundings and performs work W = 156.7 J. By the first law, the change in internal energy is ΔU = Q − W = 140.6 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
756 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1181 J, W = -286.9 J | A thermodynamic system exchanges heat Q = 1181 J with its surroundings and performs work W = -286.9 J. By the first law, the change in internal energy is ΔU = Q − W = 1468 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
757 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 254.4 J, W = -570.8 J | A thermodynamic system exchanges heat Q = 254.4 J with its surroundings and performs work W = -570.8 J. By the first law, the change in internal energy is ΔU = Q − W = 825.2 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
758 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1151 J, W = -446.3 J | A thermodynamic system exchanges heat Q = 1151 J with its surroundings and performs work W = -446.3 J. By the first law, the change in internal energy is ΔU = Q − W = 1597 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
759 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 251.3 J, W = -702.5 J | A thermodynamic system exchanges heat Q = 251.3 J with its surroundings and performs work W = -702.5 J. By the first law, the change in internal energy is ΔU = Q − W = 953.7 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
760 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1871 J, W = 607.5 J | A thermodynamic system exchanges heat Q = 1871 J with its surroundings and performs work W = 607.5 J. By the first law, the change in internal energy is ΔU = Q − W = 1264 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
761 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1779 J, W = 201.6 J | A thermodynamic system exchanges heat Q = 1779 J with its surroundings and performs work W = 201.6 J. By the first law, the change in internal energy is ΔU = Q − W = 1577 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
762 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 568 J, W = -7.007 J | A thermodynamic system exchanges heat Q = 568 J with its surroundings and performs work W = -7.007 J. By the first law, the change in internal energy is ΔU = Q − W = 575 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
763 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1931 J, W = 706.5 J | A thermodynamic system exchanges heat Q = 1931 J with its surroundings and performs work W = 706.5 J. By the first law, the change in internal energy is ΔU = Q − W = 1224 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
764 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1178 J, W = 457.3 J | A thermodynamic system exchanges heat Q = 1178 J with its surroundings and performs work W = 457.3 J. By the first law, the change in internal energy is ΔU = Q − W = 721.1 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
765 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 296.8 J, W = -133.9 J | A thermodynamic system exchanges heat Q = 296.8 J with its surroundings and performs work W = -133.9 J. By the first law, the change in internal energy is ΔU = Q − W = 430.7 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
766 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -127 J, W = -197.7 J | A thermodynamic system exchanges heat Q = -127 J with its surroundings and performs work W = -197.7 J. By the first law, the change in internal energy is ΔU = Q − W = 70.71 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
767 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1386 J, W = -42.37 J | A thermodynamic system exchanges heat Q = 1386 J with its surroundings and performs work W = -42.37 J. By the first law, the change in internal energy is ΔU = Q − W = 1428 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
768 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1623 J, W = -318.8 J | A thermodynamic system exchanges heat Q = 1623 J with its surroundings and performs work W = -318.8 J. By the first law, the change in internal energy is ΔU = Q − W = 1942 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
769 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1269 J, W = 489.2 J | A thermodynamic system exchanges heat Q = 1269 J with its surroundings and performs work W = 489.2 J. By the first law, the change in internal energy is ΔU = Q − W = 779.7 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
770 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1787 J, W = 99.82 J | A thermodynamic system exchanges heat Q = 1787 J with its surroundings and performs work W = 99.82 J. By the first law, the change in internal energy is ΔU = Q − W = 1687 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
771 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1919 J, W = 91.66 J | A thermodynamic system exchanges heat Q = 1919 J with its surroundings and performs work W = 91.66 J. By the first law, the change in internal energy is ΔU = Q − W = 1828 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
772 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -164.8 J, W = -411.4 J | A thermodynamic system exchanges heat Q = -164.8 J with its surroundings and performs work W = -411.4 J. By the first law, the change in internal energy is ΔU = Q − W = 246.7 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
773 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 8.342 J, W = 234.7 J | A thermodynamic system exchanges heat Q = 8.342 J with its surroundings and performs work W = 234.7 J. By the first law, the change in internal energy is ΔU = Q − W = -226.4 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
774 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1806 J, W = 555.4 J | A thermodynamic system exchanges heat Q = 1806 J with its surroundings and performs work W = 555.4 J. By the first law, the change in internal energy is ΔU = Q − W = 1250 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
775 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -268.8 J, W = 359.3 J | A thermodynamic system exchanges heat Q = -268.8 J with its surroundings and performs work W = 359.3 J. By the first law, the change in internal energy is ΔU = Q − W = -628.2 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
776 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -23.8 J, W = -370.5 J | A thermodynamic system exchanges heat Q = -23.8 J with its surroundings and performs work W = -370.5 J. By the first law, the change in internal energy is ΔU = Q − W = 346.7 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
777 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1184 J, W = 164.7 J | A thermodynamic system exchanges heat Q = 1184 J with its surroundings and performs work W = 164.7 J. By the first law, the change in internal energy is ΔU = Q − W = 1020 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
778 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1684 J, W = -498.9 J | A thermodynamic system exchanges heat Q = 1684 J with its surroundings and performs work W = -498.9 J. By the first law, the change in internal energy is ΔU = Q − W = 2183 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
779 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1404 J, W = 358.9 J | A thermodynamic system exchanges heat Q = 1404 J with its surroundings and performs work W = 358.9 J. By the first law, the change in internal energy is ΔU = Q − W = 1045 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
780 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 897.1 J, W = -32.97 J | A thermodynamic system exchanges heat Q = 897.1 J with its surroundings and performs work W = -32.97 J. By the first law, the change in internal energy is ΔU = Q − W = 930.1 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
781 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1674 J, W = -267.3 J | A thermodynamic system exchanges heat Q = 1674 J with its surroundings and performs work W = -267.3 J. By the first law, the change in internal energy is ΔU = Q − W = 1941 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
782 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1893 J, W = -775.5 J | A thermodynamic system exchanges heat Q = 1893 J with its surroundings and performs work W = -775.5 J. By the first law, the change in internal energy is ΔU = Q − W = 2668 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
783 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1843 J, W = 739.3 J | A thermodynamic system exchanges heat Q = 1843 J with its surroundings and performs work W = 739.3 J. By the first law, the change in internal energy is ΔU = Q − W = 1104 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
784 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -206.7 J, W = 799.3 J | A thermodynamic system exchanges heat Q = -206.7 J with its surroundings and performs work W = 799.3 J. By the first law, the change in internal energy is ΔU = Q − W = -1006 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
785 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 697.3 J, W = -411.9 J | A thermodynamic system exchanges heat Q = 697.3 J with its surroundings and performs work W = -411.9 J. By the first law, the change in internal energy is ΔU = Q − W = 1109 J. The first law is a statement of conservation of energy applied to thermodynamic systems; internal energy is a state function. | ΔU = Q - W | mechanical_energy | Apply the first law of thermodynamics to compute the change in internal energy. |
786 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.6137 c | A clock moving at velocity v = 0.6137 c relative to an inertial observer measures a proper time interval Δτ = 2.045 s. The observer measures a dilated interval Δt = γ Δτ = 2.59 s, where γ = 1 / sqrt(1 − v²/c²) = 1.267. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
787 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.8779 c | A clock moving at velocity v = 0.8779 c relative to an inertial observer measures a proper time interval Δτ = 5.521 s. The observer measures a dilated interval Δt = γ Δτ = 11.53 s, where γ = 1 / sqrt(1 − v²/c²) = 2.088. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
788 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.7592 c | A clock moving at velocity v = 0.7592 c relative to an inertial observer measures a proper time interval Δτ = 3.807 s. The observer measures a dilated interval Δt = γ Δτ = 5.848 s, where γ = 1 / sqrt(1 − v²/c²) = 1.536. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
789 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.5536 c | A clock moving at velocity v = 0.5536 c relative to an inertial observer measures a proper time interval Δτ = 3.593 s. The observer measures a dilated interval Δt = γ Δτ = 4.314 s, where γ = 1 / sqrt(1 − v²/c²) = 1.201. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
790 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.3223 c | A clock moving at velocity v = 0.3223 c relative to an inertial observer measures a proper time interval Δτ = 5.128 s. The observer measures a dilated interval Δt = γ Δτ = 5.417 s, where γ = 1 / sqrt(1 − v²/c²) = 1.056. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
791 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.5227 c | A clock moving at velocity v = 0.5227 c relative to an inertial observer measures a proper time interval Δτ = 0.9861 s. The observer measures a dilated interval Δt = γ Δτ = 1.157 s, where γ = 1 / sqrt(1 − v²/c²) = 1.173. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
792 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.9341 c | A clock moving at velocity v = 0.9341 c relative to an inertial observer measures a proper time interval Δτ = 4.695 s. The observer measures a dilated interval Δt = γ Δτ = 13.15 s, where γ = 1 / sqrt(1 − v²/c²) = 2.801. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
793 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.8138 c | A clock moving at velocity v = 0.8138 c relative to an inertial observer measures a proper time interval Δτ = 9.143 s. The observer measures a dilated interval Δt = γ Δτ = 15.73 s, where γ = 1 / sqrt(1 − v²/c²) = 1.721. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
794 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.4151 c | A clock moving at velocity v = 0.4151 c relative to an inertial observer measures a proper time interval Δτ = 4.139 s. The observer measures a dilated interval Δt = γ Δτ = 4.55 s, where γ = 1 / sqrt(1 − v²/c²) = 1.099. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
795 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.5781 c | A clock moving at velocity v = 0.5781 c relative to an inertial observer measures a proper time interval Δτ = 2.213 s. The observer measures a dilated interval Δt = γ Δτ = 2.712 s, where γ = 1 / sqrt(1 − v²/c²) = 1.226. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
796 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.224 c | A clock moving at velocity v = 0.224 c relative to an inertial observer measures a proper time interval Δτ = 2.608 s. The observer measures a dilated interval Δt = γ Δτ = 2.676 s, where γ = 1 / sqrt(1 − v²/c²) = 1.026. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
797 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.8945 c | A clock moving at velocity v = 0.8945 c relative to an inertial observer measures a proper time interval Δτ = 5.791 s. The observer measures a dilated interval Δt = γ Δτ = 12.96 s, where γ = 1 / sqrt(1 − v²/c²) = 2.237. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
798 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.4549 c | A clock moving at velocity v = 0.4549 c relative to an inertial observer measures a proper time interval Δτ = 1.524 s. The observer measures a dilated interval Δt = γ Δτ = 1.711 s, where γ = 1 / sqrt(1 − v²/c²) = 1.123. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
799 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.3804 c | A clock moving at velocity v = 0.3804 c relative to an inertial observer measures a proper time interval Δτ = 3.798 s. The observer measures a dilated interval Δt = γ Δτ = 4.107 s, where γ = 1 / sqrt(1 − v²/c²) = 1.081. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
800 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.8084 c | A clock moving at velocity v = 0.8084 c relative to an inertial observer measures a proper time interval Δτ = 4.993 s. The observer measures a dilated interval Δt = γ Δτ = 8.482 s, where γ = 1 / sqrt(1 − v²/c²) = 1.699. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.