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2,401 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1499e+04 Hz, speed 829.1 m/s | A periodic wave travels at speed v = 829.1 m/s with frequency f = 1.1499e+04 Hz. The wavelength is λ = v / f = 0.0721 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. |
2,402 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 7406 Hz, speed 546.2 m/s | A periodic wave travels at speed v = 546.2 m/s with frequency f = 7406 Hz. The wavelength is λ = v / f = 0.07375 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. |
2,403 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4149e+04 Hz, speed 1099 m/s | A periodic wave travels at speed v = 1099 m/s with frequency f = 1.4149e+04 Hz. The wavelength is λ = v / f = 0.07765 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. |
2,404 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9561e+04 Hz, speed 477.5 m/s | A periodic wave travels at speed v = 477.5 m/s with frequency f = 1.9561e+04 Hz. The wavelength is λ = v / f = 0.02441 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. |
2,405 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 8980 Hz, speed 1471 m/s | A periodic wave travels at speed v = 1471 m/s with frequency f = 8980 Hz. The wavelength is λ = v / f = 0.1638 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. |
2,406 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0682e+04 Hz, speed 445.8 m/s | A periodic wave travels at speed v = 445.8 m/s with frequency f = 1.0682e+04 Hz. The wavelength is λ = v / f = 0.04173 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. |
2,407 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 518 Hz, speed 1417 m/s | A periodic wave travels at speed v = 1417 m/s with frequency f = 518 Hz. The wavelength is λ = v / f = 2.736 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. |
2,408 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.5375e+04 Hz, speed 1437 m/s | A periodic wave travels at speed v = 1437 m/s with frequency f = 1.5375e+04 Hz. The wavelength is λ = v / f = 0.09349 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. |
2,409 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.8558e+04 Hz, speed 487.3 m/s | A periodic wave travels at speed v = 487.3 m/s with frequency f = 1.8558e+04 Hz. The wavelength is λ = v / f = 0.02626 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. |
2,410 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9404e+04 Hz, speed 955.4 m/s | A periodic wave travels at speed v = 955.4 m/s with frequency f = 1.9404e+04 Hz. The wavelength is λ = v / f = 0.04924 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. |
2,411 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0158e+04 Hz, speed 1077 m/s | A periodic wave travels at speed v = 1077 m/s with frequency f = 1.0158e+04 Hz. The wavelength is λ = v / f = 0.106 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. |
2,412 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5925 Hz, speed 1375 m/s | A periodic wave travels at speed v = 1375 m/s with frequency f = 5925 Hz. The wavelength is λ = v / f = 0.2321 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. |
2,413 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9393e+04 Hz, speed 1205 m/s | A periodic wave travels at speed v = 1205 m/s with frequency f = 1.9393e+04 Hz. The wavelength is λ = v / f = 0.06214 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. |
2,414 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9881e+04 Hz, speed 1100 m/s | A periodic wave travels at speed v = 1100 m/s with frequency f = 1.9881e+04 Hz. The wavelength is λ = v / f = 0.05534 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. |
2,415 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.5996e+04 Hz, speed 1174 m/s | A periodic wave travels at speed v = 1174 m/s with frequency f = 1.5996e+04 Hz. The wavelength is λ = v / f = 0.07341 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. |
2,416 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.8447e+04 Hz, speed 706.4 m/s | A periodic wave travels at speed v = 706.4 m/s with frequency f = 1.8447e+04 Hz. The wavelength is λ = v / f = 0.03829 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. |
2,417 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 2264 Hz, speed 874.8 m/s | A periodic wave travels at speed v = 874.8 m/s with frequency f = 2264 Hz. The wavelength is λ = v / f = 0.3864 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. |
2,418 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 820.8 Hz, speed 1114 m/s | A periodic wave travels at speed v = 1114 m/s with frequency f = 820.8 Hz. The wavelength is λ = v / f = 1.357 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. |
2,419 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 2355 Hz, speed 329.8 m/s | A periodic wave travels at speed v = 329.8 m/s with frequency f = 2355 Hz. The wavelength is λ = v / f = 0.14 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. |
2,420 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.2358e+04 Hz, speed 564.4 m/s | A periodic wave travels at speed v = 564.4 m/s with frequency f = 1.2358e+04 Hz. The wavelength is λ = v / f = 0.04567 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. |
2,421 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 7161 Hz, speed 691.6 m/s | A periodic wave travels at speed v = 691.6 m/s with frequency f = 7161 Hz. The wavelength is λ = v / f = 0.09659 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. |
2,422 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.2171e+04 Hz, speed 534.2 m/s | A periodic wave travels at speed v = 534.2 m/s with frequency f = 1.2171e+04 Hz. The wavelength is λ = v / f = 0.04389 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. |
2,423 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0538e+04 Hz, speed 1238 m/s | A periodic wave travels at speed v = 1238 m/s with frequency f = 1.0538e+04 Hz. The wavelength is λ = v / f = 0.1174 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. |
2,424 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.5347e+04 Hz, speed 534.9 m/s | A periodic wave travels at speed v = 534.9 m/s with frequency f = 1.5347e+04 Hz. The wavelength is λ = v / f = 0.03485 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. |
2,425 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1690 Hz, speed 1319 m/s | A periodic wave travels at speed v = 1319 m/s with frequency f = 1690 Hz. The wavelength is λ = v / f = 0.7806 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. |
2,426 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3548e+04 Hz, speed 1449 m/s | A periodic wave travels at speed v = 1449 m/s with frequency f = 1.3548e+04 Hz. The wavelength is λ = v / f = 0.107 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. |
2,427 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9517e+04 Hz, speed 773.3 m/s | A periodic wave travels at speed v = 773.3 m/s with frequency f = 1.9517e+04 Hz. The wavelength is λ = v / f = 0.03962 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. |
2,428 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9819 Hz, speed 1024 m/s | A periodic wave travels at speed v = 1024 m/s with frequency f = 9819 Hz. The wavelength is λ = v / f = 0.1043 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. |
2,429 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0241e+04 Hz, speed 367.3 m/s | A periodic wave travels at speed v = 367.3 m/s with frequency f = 1.0241e+04 Hz. The wavelength is λ = v / f = 0.03586 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. |
2,430 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3342e+04 Hz, speed 777.1 m/s | A periodic wave travels at speed v = 777.1 m/s with frequency f = 1.3342e+04 Hz. The wavelength is λ = v / f = 0.05824 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. |
2,431 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4325e+04 Hz, speed 813.2 m/s | A periodic wave travels at speed v = 813.2 m/s with frequency f = 1.4325e+04 Hz. The wavelength is λ = v / f = 0.05677 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. |
2,432 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 7735 Hz, speed 314.6 m/s | A periodic wave travels at speed v = 314.6 m/s with frequency f = 7735 Hz. The wavelength is λ = v / f = 0.04068 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. |
2,433 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 6912 Hz, speed 669.7 m/s | A periodic wave travels at speed v = 669.7 m/s with frequency f = 6912 Hz. The wavelength is λ = v / f = 0.0969 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. |
2,434 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 8923 Hz, speed 973.2 m/s | A periodic wave travels at speed v = 973.2 m/s with frequency f = 8923 Hz. The wavelength is λ = v / f = 0.1091 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. |
2,435 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 4330 Hz, speed 1365 m/s | A periodic wave travels at speed v = 1365 m/s with frequency f = 4330 Hz. The wavelength is λ = v / f = 0.3154 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. |
2,436 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4836e+04 Hz, speed 798.7 m/s | A periodic wave travels at speed v = 798.7 m/s with frequency f = 1.4836e+04 Hz. The wavelength is λ = v / f = 0.05384 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. |
2,437 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 8861 Hz, speed 496.5 m/s | A periodic wave travels at speed v = 496.5 m/s with frequency f = 8861 Hz. The wavelength is λ = v / f = 0.05604 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. |
2,438 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4565e+04 Hz, speed 1377 m/s | A periodic wave travels at speed v = 1377 m/s with frequency f = 1.4565e+04 Hz. The wavelength is λ = v / f = 0.09456 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. |
2,439 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4578e+04 Hz, speed 797 m/s | A periodic wave travels at speed v = 797 m/s with frequency f = 1.4578e+04 Hz. The wavelength is λ = v / f = 0.05468 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. |
2,440 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.6714e+04 Hz, speed 1018 m/s | A periodic wave travels at speed v = 1018 m/s with frequency f = 1.6714e+04 Hz. The wavelength is λ = v / f = 0.06088 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. |
2,441 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 2890 Hz, speed 663.9 m/s | A periodic wave travels at speed v = 663.9 m/s with frequency f = 2890 Hz. The wavelength is λ = v / f = 0.2297 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. |
2,442 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9768e+04 Hz, speed 930.4 m/s | A periodic wave travels at speed v = 930.4 m/s with frequency f = 1.9768e+04 Hz. The wavelength is λ = v / f = 0.04706 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. |
2,443 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 6722 Hz, speed 1420 m/s | A periodic wave travels at speed v = 1420 m/s with frequency f = 6722 Hz. The wavelength is λ = v / f = 0.2112 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. |
2,444 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1822e+04 Hz, speed 750.9 m/s | A periodic wave travels at speed v = 750.9 m/s with frequency f = 1.1822e+04 Hz. The wavelength is λ = v / f = 0.06352 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. |
2,445 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 152.2 Hz, speed 1067 m/s | A periodic wave travels at speed v = 1067 m/s with frequency f = 152.2 Hz. The wavelength is λ = v / f = 7.006 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. |
2,446 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5481 Hz, speed 509.9 m/s | A periodic wave travels at speed v = 509.9 m/s with frequency f = 5481 Hz. The wavelength is λ = v / f = 0.09302 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. |
2,447 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9253 Hz, speed 981.5 m/s | A periodic wave travels at speed v = 981.5 m/s with frequency f = 9253 Hz. The wavelength is λ = v / f = 0.1061 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. |
2,448 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.8299e+04 Hz, speed 539.1 m/s | A periodic wave travels at speed v = 539.1 m/s with frequency f = 1.8299e+04 Hz. The wavelength is λ = v / f = 0.02946 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. |
2,449 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.6649e+04 Hz, speed 647.4 m/s | A periodic wave travels at speed v = 647.4 m/s with frequency f = 1.6649e+04 Hz. The wavelength is λ = v / f = 0.03888 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. |
2,450 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9822 Hz, speed 1287 m/s | A periodic wave travels at speed v = 1287 m/s with frequency f = 9822 Hz. The wavelength is λ = v / f = 0.1311 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. |
2,451 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 6054 Hz, speed 1002 m/s | A periodic wave travels at speed v = 1002 m/s with frequency f = 6054 Hz. The wavelength is λ = v / f = 0.1656 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. |
2,452 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9892 Hz, speed 1188 m/s | A periodic wave travels at speed v = 1188 m/s with frequency f = 9892 Hz. The wavelength is λ = v / f = 0.1201 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. |
2,453 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 61.3 J, W = 466 J | A thermodynamic system exchanges heat Q = 61.3 J with its surroundings and performs work W = 466 J. By the first law, the change in internal energy is ΔU = Q − W = -404.7 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. |
2,454 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -114.9 J, W = -319.7 J | A thermodynamic system exchanges heat Q = -114.9 J with its surroundings and performs work W = -319.7 J. By the first law, the change in internal energy is ΔU = Q − W = 204.8 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. |
2,455 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1101 J, W = 218.5 J | A thermodynamic system exchanges heat Q = 1101 J with its surroundings and performs work W = 218.5 J. By the first law, the change in internal energy is ΔU = Q − W = 882.9 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. |
2,456 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -189.6 J, W = 265.5 J | A thermodynamic system exchanges heat Q = -189.6 J with its surroundings and performs work W = 265.5 J. By the first law, the change in internal energy is ΔU = Q − W = -455 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. |
2,457 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 219.2 J, W = -513 J | A thermodynamic system exchanges heat Q = 219.2 J with its surroundings and performs work W = -513 J. By the first law, the change in internal energy is ΔU = Q − W = 732.2 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. |
2,458 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1767 J, W = 231.7 J | A thermodynamic system exchanges heat Q = 1767 J with its surroundings and performs work W = 231.7 J. By the first law, the change in internal energy is ΔU = Q − W = 1535 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. |
2,459 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -428.9 J, W = 423.5 J | A thermodynamic system exchanges heat Q = -428.9 J with its surroundings and performs work W = 423.5 J. By the first law, the change in internal energy is ΔU = Q − W = -852.4 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. |
2,460 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 732.6 J, W = 753 J | A thermodynamic system exchanges heat Q = 732.6 J with its surroundings and performs work W = 753 J. By the first law, the change in internal energy is ΔU = Q − W = -20.37 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. |
2,461 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 997.2 J, W = -221.2 J | A thermodynamic system exchanges heat Q = 997.2 J with its surroundings and performs work W = -221.2 J. By the first law, the change in internal energy is ΔU = Q − W = 1218 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. |
2,462 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 701.2 J, W = -102.3 J | A thermodynamic system exchanges heat Q = 701.2 J with its surroundings and performs work W = -102.3 J. By the first law, the change in internal energy is ΔU = Q − W = 803.5 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. |
2,463 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 144.8 J, W = 297.5 J | A thermodynamic system exchanges heat Q = 144.8 J with its surroundings and performs work W = 297.5 J. By the first law, the change in internal energy is ΔU = Q − W = -152.7 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. |
2,464 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1936 J, W = 509.2 J | A thermodynamic system exchanges heat Q = 1936 J with its surroundings and performs work W = 509.2 J. By the first law, the change in internal energy is ΔU = Q − W = 1426 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. |
2,465 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 433 J, W = 372.7 J | A thermodynamic system exchanges heat Q = 433 J with its surroundings and performs work W = 372.7 J. By the first law, the change in internal energy is ΔU = Q − W = 60.27 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. |
2,466 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -456.1 J, W = -384.7 J | A thermodynamic system exchanges heat Q = -456.1 J with its surroundings and performs work W = -384.7 J. By the first law, the change in internal energy is ΔU = Q − W = -71.4 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. |
2,467 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 954.1 J, W = -566.2 J | A thermodynamic system exchanges heat Q = 954.1 J with its surroundings and performs work W = -566.2 J. By the first law, the change in internal energy is ΔU = Q − W = 1520 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. |
2,468 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 652.6 J, W = 309.3 J | A thermodynamic system exchanges heat Q = 652.6 J with its surroundings and performs work W = 309.3 J. By the first law, the change in internal energy is ΔU = Q − W = 343.4 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. |
2,469 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 393.5 J, W = -715.4 J | A thermodynamic system exchanges heat Q = 393.5 J with its surroundings and performs work W = -715.4 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. |
2,470 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 402.9 J, W = 218 J | A thermodynamic system exchanges heat Q = 402.9 J with its surroundings and performs work W = 218 J. By the first law, the change in internal energy is ΔU = Q − W = 184.9 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. |
2,471 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1888 J, W = -722.1 J | A thermodynamic system exchanges heat Q = 1888 J with its surroundings and performs work W = -722.1 J. By the first law, the change in internal energy is ΔU = Q − W = 2610 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. |
2,472 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 229.2 J, W = 222.3 J | A thermodynamic system exchanges heat Q = 229.2 J with its surroundings and performs work W = 222.3 J. By the first law, the change in internal energy is ΔU = Q − W = 6.846 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. |
2,473 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -307.9 J, W = -489.9 J | A thermodynamic system exchanges heat Q = -307.9 J with its surroundings and performs work W = -489.9 J. By the first law, the change in internal energy is ΔU = Q − W = 182 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. |
2,474 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1070 J, W = 423.5 J | A thermodynamic system exchanges heat Q = 1070 J with its surroundings and performs work W = 423.5 J. By the first law, the change in internal energy is ΔU = Q − W = 646.6 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. |
2,475 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 996.9 J, W = -532.6 J | A thermodynamic system exchanges heat Q = 996.9 J with its surroundings and performs work W = -532.6 J. By the first law, the change in internal energy is ΔU = Q − W = 1529 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. |
2,476 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 306.5 J, W = -294.1 J | A thermodynamic system exchanges heat Q = 306.5 J with its surroundings and performs work W = -294.1 J. By the first law, the change in internal energy is ΔU = Q − W = 600.6 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. |
2,477 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1612 J, W = 479.8 J | A thermodynamic system exchanges heat Q = 1612 J with its surroundings and performs work W = 479.8 J. By the first law, the change in internal energy is ΔU = Q − W = 1133 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. |
2,478 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 178.6 J, W = 316.7 J | A thermodynamic system exchanges heat Q = 178.6 J with its surroundings and performs work W = 316.7 J. By the first law, the change in internal energy is ΔU = Q − W = -138.1 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. |
2,479 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 406.3 J, W = 55.07 J | A thermodynamic system exchanges heat Q = 406.3 J with its surroundings and performs work W = 55.07 J. By the first law, the change in internal energy is ΔU = Q − W = 351.2 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. |
2,480 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 379.1 J, W = -570.1 J | A thermodynamic system exchanges heat Q = 379.1 J with its surroundings and performs work W = -570.1 J. By the first law, the change in internal energy is ΔU = Q − W = 949.1 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. |
2,481 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -157.6 J, W = -349.7 J | A thermodynamic system exchanges heat Q = -157.6 J with its surroundings and performs work W = -349.7 J. By the first law, the change in internal energy is ΔU = Q − W = 192.1 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. |
2,482 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1447 J, W = -140.8 J | A thermodynamic system exchanges heat Q = 1447 J with its surroundings and performs work W = -140.8 J. By the first law, the change in internal energy is ΔU = Q − W = 1588 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. |
2,483 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1802 J, W = -539.2 J | A thermodynamic system exchanges heat Q = 1802 J with its surroundings and performs work W = -539.2 J. By the first law, the change in internal energy is ΔU = Q − W = 2341 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. |
2,484 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 44.69 J, W = 5.413 J | A thermodynamic system exchanges heat Q = 44.69 J with its surroundings and performs work W = 5.413 J. By the first law, the change in internal energy is ΔU = Q − W = 39.28 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. |
2,485 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1579 J, W = 472.2 J | A thermodynamic system exchanges heat Q = 1579 J with its surroundings and performs work W = 472.2 J. By the first law, the change in internal energy is ΔU = Q − W = 1107 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. |
2,486 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 896.6 J, W = 303.4 J | A thermodynamic system exchanges heat Q = 896.6 J with its surroundings and performs work W = 303.4 J. By the first law, the change in internal energy is ΔU = Q − W = 593.2 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. |
2,487 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1881 J, W = 553.7 J | A thermodynamic system exchanges heat Q = 1881 J with its surroundings and performs work W = 553.7 J. By the first law, the change in internal energy is ΔU = Q − W = 1328 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. |
2,488 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1281 J, W = 323.6 J | A thermodynamic system exchanges heat Q = 1281 J with its surroundings and performs work W = 323.6 J. By the first law, the change in internal energy is ΔU = Q − W = 957.7 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. |
2,489 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1506 J, W = -132.2 J | A thermodynamic system exchanges heat Q = 1506 J with its surroundings and performs work W = -132.2 J. By the first law, the change in internal energy is ΔU = Q − W = 1639 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. |
2,490 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1790 J, W = -613.5 J | A thermodynamic system exchanges heat Q = 1790 J with its surroundings and performs work W = -613.5 J. By the first law, the change in internal energy is ΔU = Q − W = 2404 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. |
2,491 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -171.9 J, W = -772.2 J | A thermodynamic system exchanges heat Q = -171.9 J with its surroundings and performs work W = -772.2 J. By the first law, the change in internal energy is ΔU = Q − W = 600.3 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. |
2,492 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 370.5 J, W = 305.7 J | A thermodynamic system exchanges heat Q = 370.5 J with its surroundings and performs work W = 305.7 J. By the first law, the change in internal energy is ΔU = Q − W = 64.84 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. |
2,493 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -152.5 J, W = -92.9 J | A thermodynamic system exchanges heat Q = -152.5 J with its surroundings and performs work W = -92.9 J. By the first law, the change in internal energy is ΔU = Q − W = -59.57 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. |
2,494 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1969 J, W = 36.99 J | A thermodynamic system exchanges heat Q = 1969 J with its surroundings and performs work W = 36.99 J. By the first law, the change in internal energy is ΔU = Q − W = 1932 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. |
2,495 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1925 J, W = -524.5 J | A thermodynamic system exchanges heat Q = 1925 J with its surroundings and performs work W = -524.5 J. By the first law, the change in internal energy is ΔU = Q − W = 2450 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. |
2,496 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 261.7 J, W = 391.1 J | A thermodynamic system exchanges heat Q = 261.7 J with its surroundings and performs work W = 391.1 J. By the first law, the change in internal energy is ΔU = Q − W = -129.4 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. |
2,497 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -203.5 J, W = -594.1 J | A thermodynamic system exchanges heat Q = -203.5 J with its surroundings and performs work W = -594.1 J. By the first law, the change in internal energy is ΔU = Q − W = 390.5 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. |
2,498 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1236 J, W = 300.9 J | A thermodynamic system exchanges heat Q = 1236 J with its surroundings and performs work W = 300.9 J. By the first law, the change in internal energy is ΔU = Q − W = 934.7 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. |
2,499 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 268.6 J, W = -464.3 J | A thermodynamic system exchanges heat Q = 268.6 J with its surroundings and performs work W = -464.3 J. By the first law, the change in internal energy is ΔU = Q − W = 732.8 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. |
2,500 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1953 J, W = -120.3 J | A thermodynamic system exchanges heat Q = 1953 J with its surroundings and performs work W = -120.3 J. By the first law, the change in internal energy is ΔU = Q − W = 2073 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. |
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