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 |
|---|---|---|---|---|---|---|---|---|---|---|
5,901 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.5436e+04 Hz, speed 1463 m/s | A periodic wave travels at speed v = 1463 m/s with frequency f = 1.5436e+04 Hz. The wavelength is λ = v / f = 0.09479 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. |
5,902 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 4050 Hz, speed 477.4 m/s | A periodic wave travels at speed v = 477.4 m/s with frequency f = 4050 Hz. The wavelength is λ = v / f = 0.1179 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. |
5,903 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3614e+04 Hz, speed 1329 m/s | A periodic wave travels at speed v = 1329 m/s with frequency f = 1.3614e+04 Hz. The wavelength is λ = v / f = 0.09765 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. |
5,904 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4886e+04 Hz, speed 628.1 m/s | A periodic wave travels at speed v = 628.1 m/s with frequency f = 1.4886e+04 Hz. The wavelength is λ = v / f = 0.0422 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. |
5,905 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 7826 Hz, speed 934.5 m/s | A periodic wave travels at speed v = 934.5 m/s with frequency f = 7826 Hz. The wavelength is λ = v / f = 0.1194 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. |
5,906 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1818e+04 Hz, speed 1412 m/s | A periodic wave travels at speed v = 1412 m/s with frequency f = 1.1818e+04 Hz. The wavelength is λ = v / f = 0.1195 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. |
5,907 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3949 Hz, speed 1224 m/s | A periodic wave travels at speed v = 1224 m/s with frequency f = 3949 Hz. The wavelength is λ = v / f = 0.3098 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. |
5,908 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4631e+04 Hz, speed 347.3 m/s | A periodic wave travels at speed v = 347.3 m/s with frequency f = 1.4631e+04 Hz. The wavelength is λ = v / f = 0.02374 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. |
5,909 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9284e+04 Hz, speed 1009 m/s | A periodic wave travels at speed v = 1009 m/s with frequency f = 1.9284e+04 Hz. The wavelength is λ = v / f = 0.05233 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. |
5,910 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5818 Hz, speed 1496 m/s | A periodic wave travels at speed v = 1496 m/s with frequency f = 5818 Hz. The wavelength is λ = v / f = 0.2572 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. |
5,911 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9140 Hz, speed 641.4 m/s | A periodic wave travels at speed v = 641.4 m/s with frequency f = 9140 Hz. The wavelength is λ = v / f = 0.07018 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. |
5,912 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 377.9 Hz, speed 1007 m/s | A periodic wave travels at speed v = 1007 m/s with frequency f = 377.9 Hz. The wavelength is λ = v / f = 2.665 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. |
5,913 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9302e+04 Hz, speed 375.4 m/s | A periodic wave travels at speed v = 375.4 m/s with frequency f = 1.9302e+04 Hz. The wavelength is λ = v / f = 0.01945 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. |
5,914 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.6594e+04 Hz, speed 800.7 m/s | A periodic wave travels at speed v = 800.7 m/s with frequency f = 1.6594e+04 Hz. The wavelength is λ = v / f = 0.04825 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. |
5,915 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9282 Hz, speed 1361 m/s | A periodic wave travels at speed v = 1361 m/s with frequency f = 9282 Hz. The wavelength is λ = v / f = 0.1467 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. |
5,916 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1447e+04 Hz, speed 1408 m/s | A periodic wave travels at speed v = 1408 m/s with frequency f = 1.1447e+04 Hz. The wavelength is λ = v / f = 0.123 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. |
5,917 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.6699e+04 Hz, speed 567.5 m/s | A periodic wave travels at speed v = 567.5 m/s with frequency f = 1.6699e+04 Hz. The wavelength is λ = v / f = 0.03398 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. |
5,918 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5309 Hz, speed 1370 m/s | A periodic wave travels at speed v = 1370 m/s with frequency f = 5309 Hz. The wavelength is λ = v / f = 0.258 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. |
5,919 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.7046e+04 Hz, speed 1280 m/s | A periodic wave travels at speed v = 1280 m/s with frequency f = 1.7046e+04 Hz. The wavelength is λ = v / f = 0.07509 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. |
5,920 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3375e+04 Hz, speed 995.5 m/s | A periodic wave travels at speed v = 995.5 m/s with frequency f = 1.3375e+04 Hz. The wavelength is λ = v / f = 0.07443 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. |
5,921 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 7908 Hz, speed 305.1 m/s | A periodic wave travels at speed v = 305.1 m/s with frequency f = 7908 Hz. The wavelength is λ = v / f = 0.03858 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. |
5,922 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 4600 Hz, speed 566.2 m/s | A periodic wave travels at speed v = 566.2 m/s with frequency f = 4600 Hz. The wavelength is λ = v / f = 0.1231 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. |
5,923 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.6434e+04 Hz, speed 586.8 m/s | A periodic wave travels at speed v = 586.8 m/s with frequency f = 1.6434e+04 Hz. The wavelength is λ = v / f = 0.03571 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. |
5,924 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 64.96 Hz, speed 357.3 m/s | A periodic wave travels at speed v = 357.3 m/s with frequency f = 64.96 Hz. The wavelength is λ = v / f = 5.5 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. |
5,925 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1541 Hz, speed 1264 m/s | A periodic wave travels at speed v = 1264 m/s with frequency f = 1541 Hz. The wavelength is λ = v / f = 0.8204 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. |
5,926 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0714e+04 Hz, speed 1379 m/s | A periodic wave travels at speed v = 1379 m/s with frequency f = 1.0714e+04 Hz. The wavelength is λ = v / f = 0.1287 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. |
5,927 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1850 J, W = -773.9 J | A thermodynamic system exchanges heat Q = 1850 J with its surroundings and performs work W = -773.9 J. By the first law, the change in internal energy is ΔU = Q − W = 2624 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. |
5,928 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1671 J, W = 372.4 J | A thermodynamic system exchanges heat Q = 1671 J with its surroundings and performs work W = 372.4 J. By the first law, the change in internal energy is ΔU = Q − W = 1299 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. |
5,929 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1417 J, W = 460.8 J | A thermodynamic system exchanges heat Q = 1417 J with its surroundings and performs work W = 460.8 J. By the first law, the change in internal energy is ΔU = Q − W = 956.2 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. |
5,930 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1422 J, W = 261.3 J | A thermodynamic system exchanges heat Q = 1422 J with its surroundings and performs work W = 261.3 J. By the first law, the change in internal energy is ΔU = Q − W = 1161 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. |
5,931 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 741.6 J, W = 128.3 J | A thermodynamic system exchanges heat Q = 741.6 J with its surroundings and performs work W = 128.3 J. By the first law, the change in internal energy is ΔU = Q − W = 613.3 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. |
5,932 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 835.2 J, W = 83.77 J | A thermodynamic system exchanges heat Q = 835.2 J with its surroundings and performs work W = 83.77 J. By the first law, the change in internal energy is ΔU = Q − W = 751.5 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. |
5,933 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1449 J, W = 568.4 J | A thermodynamic system exchanges heat Q = 1449 J with its surroundings and performs work W = 568.4 J. By the first law, the change in internal energy is ΔU = Q − W = 880.8 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. |
5,934 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1814 J, W = -177.6 J | A thermodynamic system exchanges heat Q = 1814 J with its surroundings and performs work W = -177.6 J. By the first law, the change in internal energy is ΔU = Q − W = 1992 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. |
5,935 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1314 J, W = -516.4 J | A thermodynamic system exchanges heat Q = 1314 J with its surroundings and performs work W = -516.4 J. By the first law, the change in internal energy is ΔU = Q − W = 1831 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. |
5,936 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1140 J, W = -777.3 J | A thermodynamic system exchanges heat Q = 1140 J with its surroundings and performs work W = -777.3 J. By the first law, the change in internal energy is ΔU = Q − W = 1918 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. |
5,937 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 573.8 J, W = -274 J | A thermodynamic system exchanges heat Q = 573.8 J with its surroundings and performs work W = -274 J. By the first law, the change in internal energy is ΔU = Q − W = 847.7 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. |
5,938 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 114 J, W = -32.22 J | A thermodynamic system exchanges heat Q = 114 J with its surroundings and performs work W = -32.22 J. By the first law, the change in internal energy is ΔU = Q − W = 146.2 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. |
5,939 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -251.4 J, W = 689.7 J | A thermodynamic system exchanges heat Q = -251.4 J with its surroundings and performs work W = 689.7 J. By the first law, the change in internal energy is ΔU = Q − W = -941.1 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. |
5,940 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1328 J, W = -529.6 J | A thermodynamic system exchanges heat Q = 1328 J with its surroundings and performs work W = -529.6 J. By the first law, the change in internal energy is ΔU = Q − W = 1857 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. |
5,941 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 230.8 J, W = -388.7 J | A thermodynamic system exchanges heat Q = 230.8 J with its surroundings and performs work W = -388.7 J. By the first law, the change in internal energy is ΔU = Q − W = 619.4 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. |
5,942 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -95.35 J, W = -117.7 J | A thermodynamic system exchanges heat Q = -95.35 J with its surroundings and performs work W = -117.7 J. By the first law, the change in internal energy is ΔU = Q − W = 22.33 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. |
5,943 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1323 J, W = -221.7 J | A thermodynamic system exchanges heat Q = 1323 J with its surroundings and performs work W = -221.7 J. By the first law, the change in internal energy is ΔU = Q − W = 1545 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. |
5,944 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1413 J, W = -338 J | A thermodynamic system exchanges heat Q = 1413 J with its surroundings and performs work W = -338 J. By the first law, the change in internal energy is ΔU = Q − W = 1751 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. |
5,945 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1995 J, W = 306.5 J | A thermodynamic system exchanges heat Q = 1995 J with its surroundings and performs work W = 306.5 J. By the first law, the change in internal energy is ΔU = Q − W = 1688 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. |
5,946 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1098 J, W = -678 J | A thermodynamic system exchanges heat Q = 1098 J with its surroundings and performs work W = -678 J. By the first law, the change in internal energy is ΔU = Q − W = 1776 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. |
5,947 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -111.1 J, W = -605.7 J | A thermodynamic system exchanges heat Q = -111.1 J with its surroundings and performs work W = -605.7 J. By the first law, the change in internal energy is ΔU = Q − W = 494.6 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. |
5,948 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1843 J, W = 725.7 J | A thermodynamic system exchanges heat Q = 1843 J with its surroundings and performs work W = 725.7 J. By the first law, the change in internal energy is ΔU = Q − W = 1117 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. |
5,949 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -335 J, W = 432.5 J | A thermodynamic system exchanges heat Q = -335 J with its surroundings and performs work W = 432.5 J. By the first law, the change in internal energy is ΔU = Q − W = -767.6 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. |
5,950 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1396 J, W = -367.9 J | A thermodynamic system exchanges heat Q = 1396 J with its surroundings and performs work W = -367.9 J. By the first law, the change in internal energy is ΔU = Q − W = 1764 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. |
5,951 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -52.57 J, W = 423.8 J | A thermodynamic system exchanges heat Q = -52.57 J with its surroundings and performs work W = 423.8 J. By the first law, the change in internal energy is ΔU = Q − W = -476.4 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. |
5,952 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 343.8 J, W = 0.7409 J | A thermodynamic system exchanges heat Q = 343.8 J with its surroundings and performs work W = 0.7409 J. By the first law, the change in internal energy is ΔU = Q − W = 343.1 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. |
5,953 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1588 J, W = 55.35 J | A thermodynamic system exchanges heat Q = 1588 J with its surroundings and performs work W = 55.35 J. By the first law, the change in internal energy is ΔU = Q − W = 1533 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. |
5,954 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 776.9 J, W = -30.01 J | A thermodynamic system exchanges heat Q = 776.9 J with its surroundings and performs work W = -30.01 J. By the first law, the change in internal energy is ΔU = Q − W = 807 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. |
5,955 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1036 J, W = 456.8 J | A thermodynamic system exchanges heat Q = 1036 J with its surroundings and performs work W = 456.8 J. By the first law, the change in internal energy is ΔU = Q − W = 579.1 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. |
5,956 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 390.6 J, W = -652.8 J | A thermodynamic system exchanges heat Q = 390.6 J with its surroundings and performs work W = -652.8 J. By the first law, the change in internal energy is ΔU = Q − W = 1043 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. |
5,957 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -59 J, W = 490.6 J | A thermodynamic system exchanges heat Q = -59 J with its surroundings and performs work W = 490.6 J. By the first law, the change in internal energy is ΔU = Q − W = -549.6 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. |
5,958 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 863.3 J, W = -399.6 J | A thermodynamic system exchanges heat Q = 863.3 J with its surroundings and performs work W = -399.6 J. By the first law, the change in internal energy is ΔU = Q − W = 1263 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. |
5,959 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -454.4 J, W = 662.2 J | A thermodynamic system exchanges heat Q = -454.4 J with its surroundings and performs work W = 662.2 J. By the first law, the change in internal energy is ΔU = Q − W = -1117 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. |
5,960 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1511 J, W = 469.3 J | A thermodynamic system exchanges heat Q = 1511 J with its surroundings and performs work W = 469.3 J. By the first law, the change in internal energy is ΔU = Q − W = 1042 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. |
5,961 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -283.9 J, W = -698.5 J | A thermodynamic system exchanges heat Q = -283.9 J with its surroundings and performs work W = -698.5 J. By the first law, the change in internal energy is ΔU = Q − W = 414.6 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. |
5,962 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -135.5 J, W = -543.5 J | A thermodynamic system exchanges heat Q = -135.5 J with its surroundings and performs work W = -543.5 J. By the first law, the change in internal energy is ΔU = Q − W = 408 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. |
5,963 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1538 J, W = 55.69 J | A thermodynamic system exchanges heat Q = 1538 J with its surroundings and performs work W = 55.69 J. By the first law, the change in internal energy is ΔU = Q − W = 1482 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. |
5,964 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 696.7 J, W = 679.5 J | A thermodynamic system exchanges heat Q = 696.7 J with its surroundings and performs work W = 679.5 J. By the first law, the change in internal energy is ΔU = Q − W = 17.18 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. |
5,965 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1079 J, W = -752.3 J | A thermodynamic system exchanges heat Q = 1079 J with its surroundings and performs work W = -752.3 J. By the first law, the change in internal energy is ΔU = Q − W = 1831 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. |
5,966 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1634 J, W = 468.3 J | A thermodynamic system exchanges heat Q = 1634 J with its surroundings and performs work W = 468.3 J. By the first law, the change in internal energy is ΔU = Q − W = 1166 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. |
5,967 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 581 J, W = 491.6 J | A thermodynamic system exchanges heat Q = 581 J with its surroundings and performs work W = 491.6 J. By the first law, the change in internal energy is ΔU = Q − W = 89.36 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. |
5,968 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1440 J, W = -156.1 J | A thermodynamic system exchanges heat Q = 1440 J with its surroundings and performs work W = -156.1 J. By the first law, the change in internal energy is ΔU = Q − W = 1596 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. |
5,969 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -81.19 J, W = 193.7 J | A thermodynamic system exchanges heat Q = -81.19 J with its surroundings and performs work W = 193.7 J. By the first law, the change in internal energy is ΔU = Q − W = -274.9 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. |
5,970 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 708.6 J, W = 138.2 J | A thermodynamic system exchanges heat Q = 708.6 J with its surroundings and performs work W = 138.2 J. By the first law, the change in internal energy is ΔU = Q − W = 570.4 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. |
5,971 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1243 J, W = 761.8 J | A thermodynamic system exchanges heat Q = 1243 J with its surroundings and performs work W = 761.8 J. By the first law, the change in internal energy is ΔU = Q − W = 481.6 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. |
5,972 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1362 J, W = 535.2 J | A thermodynamic system exchanges heat Q = 1362 J with its surroundings and performs work W = 535.2 J. By the first law, the change in internal energy is ΔU = Q − W = 826.4 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. |
5,973 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1834 J, W = 449.2 J | A thermodynamic system exchanges heat Q = 1834 J with its surroundings and performs work W = 449.2 J. By the first law, the change in internal energy is ΔU = Q − W = 1385 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. |
5,974 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 893.6 J, W = -67.43 J | A thermodynamic system exchanges heat Q = 893.6 J with its surroundings and performs work W = -67.43 J. By the first law, the change in internal energy is ΔU = Q − W = 961.1 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. |
5,975 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 305.5 J, W = -209.8 J | A thermodynamic system exchanges heat Q = 305.5 J with its surroundings and performs work W = -209.8 J. By the first law, the change in internal energy is ΔU = Q − W = 515.3 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. |
5,976 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1750 J, W = -741.8 J | A thermodynamic system exchanges heat Q = 1750 J with its surroundings and performs work W = -741.8 J. By the first law, the change in internal energy is ΔU = Q − W = 2492 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. |
5,977 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -29.8 J, W = 113.5 J | A thermodynamic system exchanges heat Q = -29.8 J with its surroundings and performs work W = 113.5 J. By the first law, the change in internal energy is ΔU = Q − W = -143.3 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. |
5,978 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -457.2 J, W = 263.3 J | A thermodynamic system exchanges heat Q = -457.2 J with its surroundings and performs work W = 263.3 J. By the first law, the change in internal energy is ΔU = Q − W = -720.5 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. |
5,979 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 431.3 J, W = -258 J | A thermodynamic system exchanges heat Q = 431.3 J with its surroundings and performs work W = -258 J. By the first law, the change in internal energy is ΔU = Q − W = 689.4 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. |
5,980 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1374 J, W = -788.1 J | A thermodynamic system exchanges heat Q = 1374 J with its surroundings and performs work W = -788.1 J. By the first law, the change in internal energy is ΔU = Q − W = 2162 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. |
5,981 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 287.9 J, W = -58.43 J | A thermodynamic system exchanges heat Q = 287.9 J with its surroundings and performs work W = -58.43 J. By the first law, the change in internal energy is ΔU = Q − W = 346.4 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. |
5,982 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -164.8 J, W = -646.4 J | A thermodynamic system exchanges heat Q = -164.8 J with its surroundings and performs work W = -646.4 J. By the first law, the change in internal energy is ΔU = Q − W = 481.6 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. |
5,983 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 801.3 J, W = 425.8 J | A thermodynamic system exchanges heat Q = 801.3 J with its surroundings and performs work W = 425.8 J. By the first law, the change in internal energy is ΔU = Q − W = 375.5 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. |
5,984 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 982.2 J, W = -42.51 J | A thermodynamic system exchanges heat Q = 982.2 J with its surroundings and performs work W = -42.51 J. By the first law, the change in internal energy is ΔU = Q − W = 1025 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. |
5,985 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 884 J, W = 82.57 J | A thermodynamic system exchanges heat Q = 884 J with its surroundings and performs work W = 82.57 J. By the first law, the change in internal energy is ΔU = Q − W = 801.4 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. |
5,986 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1404 J, W = -608.4 J | A thermodynamic system exchanges heat Q = 1404 J with its surroundings and performs work W = -608.4 J. By the first law, the change in internal energy is ΔU = Q − W = 2012 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. |
5,987 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1527 J, W = 457.8 J | A thermodynamic system exchanges heat Q = 1527 J with its surroundings and performs work W = 457.8 J. By the first law, the change in internal energy is ΔU = Q − W = 1069 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. |
5,988 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1095 J, W = -406.3 J | A thermodynamic system exchanges heat Q = 1095 J with its surroundings and performs work W = -406.3 J. By the first law, the change in internal energy is ΔU = Q − W = 1502 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. |
5,989 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 842.7 J, W = -119 J | A thermodynamic system exchanges heat Q = 842.7 J with its surroundings and performs work W = -119 J. By the first law, the change in internal energy is ΔU = Q − W = 961.7 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. |
5,990 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -402.7 J, W = -629.5 J | A thermodynamic system exchanges heat Q = -402.7 J with its surroundings and performs work W = -629.5 J. By the first law, the change in internal energy is ΔU = Q − W = 226.8 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. |
5,991 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1848 J, W = 263.7 J | A thermodynamic system exchanges heat Q = 1848 J with its surroundings and performs work W = 263.7 J. By the first law, the change in internal energy is ΔU = Q − W = 1584 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. |
5,992 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1996 J, W = 313.5 J | A thermodynamic system exchanges heat Q = 1996 J with its surroundings and performs work W = 313.5 J. By the first law, the change in internal energy is ΔU = Q − W = 1683 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. |
5,993 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1539 J, W = 798.8 J | A thermodynamic system exchanges heat Q = 1539 J with its surroundings and performs work W = 798.8 J. By the first law, the change in internal energy is ΔU = Q − W = 740.4 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. |
5,994 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 201.7 J, W = 559.6 J | A thermodynamic system exchanges heat Q = 201.7 J with its surroundings and performs work W = 559.6 J. By the first law, the change in internal energy is ΔU = Q − W = -357.9 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. |
5,995 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1953 J, W = 760.2 J | A thermodynamic system exchanges heat Q = 1953 J with its surroundings and performs work W = 760.2 J. By the first law, the change in internal energy is ΔU = Q − W = 1193 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. |
5,996 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 409.5 J, W = -2.741 J | A thermodynamic system exchanges heat Q = 409.5 J with its surroundings and performs work W = -2.741 J. By the first law, the change in internal energy is ΔU = Q − W = 412.2 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. |
5,997 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.7278 c | A clock moving at velocity v = 0.7278 c relative to an inertial observer measures a proper time interval Δτ = 4.069 s. The observer measures a dilated interval Δt = γ Δτ = 5.933 s, where γ = 1 / sqrt(1 − v²/c²) = 1.458. 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. |
5,998 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.1222 c | A clock moving at velocity v = 0.1222 c relative to an inertial observer measures a proper time interval Δτ = 2.852 s. The observer measures a dilated interval Δt = γ Δτ = 2.873 s, where γ = 1 / sqrt(1 − v²/c²) = 1.008. 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. |
5,999 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.2571 c | A clock moving at velocity v = 0.2571 c relative to an inertial observer measures a proper time interval Δτ = 0.9308 s. The observer measures a dilated interval Δt = γ Δτ = 0.9631 s, where γ = 1 / sqrt(1 − v²/c²) = 1.035. 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. |
6,000 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.2168 c | A clock moving at velocity v = 0.2168 c relative to an inertial observer measures a proper time interval Δτ = 5.25 s. The observer measures a dilated interval Δt = γ Δτ = 5.377 s, where γ = 1 / sqrt(1 − v²/c²) = 1.024. 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.