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
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4,101 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.0176e-04 C and -2.9804e-04 C separated by 1.855 m | Two point charges q1 = -3.0176e-04 C and q2 = -2.9804e-04 C are separated by distance r = 1.855 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 234.9 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,102 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.4628e-04 C and 7.8262e-04 C separated by 1.669 m | Two point charges q1 = 5.4628e-04 C and q2 = 7.8262e-04 C are separated by distance r = 1.669 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1379 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,103 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.3947e-04 C and 6.9444e-04 C separated by 1.013 m | Two point charges q1 = -1.3947e-04 C and q2 = 6.9444e-04 C are separated by distance r = 1.013 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 849 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,104 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.6891e-04 C and 4.6709e-04 C separated by 1.923 m | Two point charges q1 = 4.6891e-04 C and q2 = 4.6709e-04 C are separated by distance r = 1.923 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 532.2 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,105 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.8645e-05 C and -9.5753e-04 C separated by 0.8476 m | Two point charges q1 = 2.8645e-05 C and q2 = -9.5753e-04 C are separated by distance r = 0.8476 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 343.1 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,106 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.1559e-04 C and 7.8685e-04 C separated by 1.165 m | Two point charges q1 = -6.1559e-04 C and q2 = 7.8685e-04 C are separated by distance r = 1.165 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3208 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,107 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.2815e-04 C and 5.4482e-05 C separated by 1.692 m | Two point charges q1 = 1.2815e-04 C and q2 = 5.4482e-05 C are separated by distance r = 1.692 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 21.92 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,108 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.0354e-04 C and -4.6335e-04 C separated by 1.528 m | Two point charges q1 = -4.0354e-04 C and q2 = -4.6335e-04 C are separated by distance r = 1.528 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 719.4 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,109 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.3936e-04 C and -5.5638e-05 C separated by 1.661 m | Two point charges q1 = 8.3936e-04 C and q2 = -5.5638e-05 C are separated by distance r = 1.661 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 152 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,110 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.3415e-04 C and -8.2212e-04 C separated by 1.135 m | Two point charges q1 = -3.3415e-04 C and q2 = -8.2212e-04 C are separated by distance r = 1.135 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1916 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,111 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.6445e-04 C and -7.4073e-04 C separated by 1.352 m | Two point charges q1 = 8.6445e-04 C and q2 = -7.4073e-04 C are separated by distance r = 1.352 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3148 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,112 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.0187e-04 C and -5.6249e-04 C separated by 1.935 m | Two point charges q1 = -7.0187e-04 C and q2 = -5.6249e-04 C are separated by distance r = 1.935 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 947.8 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,113 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.2432e-04 C and -3.0159e-04 C separated by 0.6287 m | Two point charges q1 = -2.2432e-04 C and q2 = -3.0159e-04 C are separated by distance r = 0.6287 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1538 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,114 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.0581e-04 C and -1.1559e-04 C separated by 0.01007 m | Two point charges q1 = -8.0581e-04 C and q2 = -1.1559e-04 C are separated by distance r = 0.01007 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 8.2539e+06 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,115 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.2030e-04 C and -2.0509e-04 C separated by 0.9527 m | Two point charges q1 = -5.2030e-04 C and q2 = -2.0509e-04 C are separated by distance r = 0.9527 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1057 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,116 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.9132e-04 C and -3.0062e-04 C separated by 0.9726 m | Two point charges q1 = 3.9132e-04 C and q2 = -3.0062e-04 C are separated by distance r = 0.9726 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1118 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,117 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.2045e-04 C and 8.2186e-04 C separated by 1.366 m | Two point charges q1 = -8.2045e-04 C and q2 = 8.2186e-04 C are separated by distance r = 1.366 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3249 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,118 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.3292e-04 C and -1.8562e-04 C separated by 1.639 m | Two point charges q1 = -4.3292e-04 C and q2 = -1.8562e-04 C are separated by distance r = 1.639 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 268.9 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,119 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.7160e-04 C and -4.7668e-04 C separated by 0.5872 m | Two point charges q1 = -1.7160e-04 C and q2 = -4.7668e-04 C are separated by distance r = 0.5872 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2132 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,120 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.5913e-04 C and 3.6797e-04 C separated by 0.5576 m | Two point charges q1 = -9.5913e-04 C and q2 = 3.6797e-04 C are separated by distance r = 0.5576 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.0202e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,121 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.9796e-04 C and -4.6450e-04 C separated by 1.629 m | Two point charges q1 = 6.9796e-04 C and q2 = -4.6450e-04 C are separated by distance r = 1.629 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1098 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,122 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.8943e-05 C and 1.2101e-04 C separated by 0.785 m | Two point charges q1 = -2.8943e-05 C and q2 = 1.2101e-04 C are separated by distance r = 0.785 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 51.08 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,123 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.5049e-05 C and 4.3589e-05 C separated by 1.815 m | Two point charges q1 = 3.5049e-05 C and q2 = 4.3589e-05 C are separated by distance r = 1.815 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4.168 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,124 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.6844e-04 C and 2.7763e-04 C separated by 1.964 m | Two point charges q1 = -4.6844e-04 C and q2 = 2.7763e-04 C are separated by distance r = 1.964 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 303.1 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,125 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.0114e-04 C and -3.4949e-04 C separated by 1.415 m | Two point charges q1 = 5.0114e-04 C and q2 = -3.4949e-04 C are separated by distance r = 1.415 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 785.7 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,126 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.1353e-04 C and -6.5626e-04 C separated by 0.7102 m | Two point charges q1 = 5.1353e-04 C and q2 = -6.5626e-04 C are separated by distance r = 0.7102 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6005 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,127 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.6002e-04 C and -2.7906e-04 C separated by 1.528 m | Two point charges q1 = 4.6002e-04 C and q2 = -2.7906e-04 C are separated by distance r = 1.528 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 494.4 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,128 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.2355e-04 C and -9.1624e-04 C separated by 1.294 m | Two point charges q1 = 9.2355e-04 C and q2 = -9.1624e-04 C are separated by distance r = 1.294 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4543 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,129 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.6259e-04 C and -5.7646e-04 C separated by 1.856 m | Two point charges q1 = 9.6259e-04 C and q2 = -5.7646e-04 C are separated by distance r = 1.856 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1448 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
4,130 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.5512e+04 Hz, speed 930.5 m/s | A periodic wave travels at speed v = 930.5 m/s with frequency f = 1.5512e+04 Hz. The wavelength is λ = v / f = 0.05999 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. |
4,131 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 2606 Hz, speed 688.9 m/s | A periodic wave travels at speed v = 688.9 m/s with frequency f = 2606 Hz. The wavelength is λ = v / f = 0.2644 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. |
4,132 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9105e+04 Hz, speed 717.7 m/s | A periodic wave travels at speed v = 717.7 m/s with frequency f = 1.9105e+04 Hz. The wavelength is λ = v / f = 0.03757 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. |
4,133 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.2357e+04 Hz, speed 784.5 m/s | A periodic wave travels at speed v = 784.5 m/s with frequency f = 1.2357e+04 Hz. The wavelength is λ = v / f = 0.06349 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. |
4,134 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 917.7 Hz, speed 1322 m/s | A periodic wave travels at speed v = 1322 m/s with frequency f = 917.7 Hz. The wavelength is λ = v / f = 1.441 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. |
4,135 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3200 Hz, speed 415.8 m/s | A periodic wave travels at speed v = 415.8 m/s with frequency f = 3200 Hz. The wavelength is λ = v / f = 0.1299 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. |
4,136 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 2142 Hz, speed 1421 m/s | A periodic wave travels at speed v = 1421 m/s with frequency f = 2142 Hz. The wavelength is λ = v / f = 0.6633 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. |
4,137 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9539 Hz, speed 1212 m/s | A periodic wave travels at speed v = 1212 m/s with frequency f = 9539 Hz. The wavelength is λ = v / f = 0.127 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. |
4,138 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9627e+04 Hz, speed 1270 m/s | A periodic wave travels at speed v = 1270 m/s with frequency f = 1.9627e+04 Hz. The wavelength is λ = v / f = 0.06472 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. |
4,139 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4658e+04 Hz, speed 583.9 m/s | A periodic wave travels at speed v = 583.9 m/s with frequency f = 1.4658e+04 Hz. The wavelength is λ = v / f = 0.03984 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. |
4,140 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.7998e+04 Hz, speed 508.8 m/s | A periodic wave travels at speed v = 508.8 m/s with frequency f = 1.7998e+04 Hz. The wavelength is λ = v / f = 0.02827 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. |
4,141 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.7852e+04 Hz, speed 1207 m/s | A periodic wave travels at speed v = 1207 m/s with frequency f = 1.7852e+04 Hz. The wavelength is λ = v / f = 0.06761 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. |
4,142 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 8413 Hz, speed 377.2 m/s | A periodic wave travels at speed v = 377.2 m/s with frequency f = 8413 Hz. The wavelength is λ = v / f = 0.04484 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. |
4,143 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.2246e+04 Hz, speed 437.4 m/s | A periodic wave travels at speed v = 437.4 m/s with frequency f = 1.2246e+04 Hz. The wavelength is λ = v / f = 0.03572 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. |
4,144 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.6939e+04 Hz, speed 387.5 m/s | A periodic wave travels at speed v = 387.5 m/s with frequency f = 1.6939e+04 Hz. The wavelength is λ = v / f = 0.02287 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. |
4,145 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.5272e+04 Hz, speed 1028 m/s | A periodic wave travels at speed v = 1028 m/s with frequency f = 1.5272e+04 Hz. The wavelength is λ = v / f = 0.0673 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. |
4,146 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.6817e+04 Hz, speed 1408 m/s | A periodic wave travels at speed v = 1408 m/s with frequency f = 1.6817e+04 Hz. The wavelength is λ = v / f = 0.08374 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. |
4,147 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 6437 Hz, speed 1138 m/s | A periodic wave travels at speed v = 1138 m/s with frequency f = 6437 Hz. The wavelength is λ = v / f = 0.1769 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. |
4,148 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 7565 Hz, speed 1487 m/s | A periodic wave travels at speed v = 1487 m/s with frequency f = 7565 Hz. The wavelength is λ = v / f = 0.1965 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. |
4,149 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1484e+04 Hz, speed 539.7 m/s | A periodic wave travels at speed v = 539.7 m/s with frequency f = 1.1484e+04 Hz. The wavelength is λ = v / f = 0.04699 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. |
4,150 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5065 Hz, speed 825 m/s | A periodic wave travels at speed v = 825 m/s with frequency f = 5065 Hz. The wavelength is λ = v / f = 0.1629 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. |
4,151 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5736 Hz, speed 541.4 m/s | A periodic wave travels at speed v = 541.4 m/s with frequency f = 5736 Hz. The wavelength is λ = v / f = 0.09439 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. |
4,152 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3259 Hz, speed 1277 m/s | A periodic wave travels at speed v = 1277 m/s with frequency f = 3259 Hz. The wavelength is λ = v / f = 0.3918 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. |
4,153 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.6177e+04 Hz, speed 530.8 m/s | A periodic wave travels at speed v = 530.8 m/s with frequency f = 1.6177e+04 Hz. The wavelength is λ = v / f = 0.03281 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. |
4,154 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1651e+04 Hz, speed 1055 m/s | A periodic wave travels at speed v = 1055 m/s with frequency f = 1.1651e+04 Hz. The wavelength is λ = v / f = 0.09055 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. |
4,155 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3380e+04 Hz, speed 544.2 m/s | A periodic wave travels at speed v = 544.2 m/s with frequency f = 1.3380e+04 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. |
4,156 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.6204e+04 Hz, speed 1372 m/s | A periodic wave travels at speed v = 1372 m/s with frequency f = 1.6204e+04 Hz. The wavelength is λ = v / f = 0.08467 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. |
4,157 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 7204 Hz, speed 789.6 m/s | A periodic wave travels at speed v = 789.6 m/s with frequency f = 7204 Hz. The wavelength is λ = v / f = 0.1096 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. |
4,158 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0941e+04 Hz, speed 386.4 m/s | A periodic wave travels at speed v = 386.4 m/s with frequency f = 1.0941e+04 Hz. The wavelength is λ = v / f = 0.03531 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. |
4,159 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3722 Hz, speed 1176 m/s | A periodic wave travels at speed v = 1176 m/s with frequency f = 3722 Hz. The wavelength is λ = v / f = 0.3159 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. |
4,160 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.8222e+04 Hz, speed 1071 m/s | A periodic wave travels at speed v = 1071 m/s with frequency f = 1.8222e+04 Hz. The wavelength is λ = v / f = 0.05876 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. |
4,161 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9934 Hz, speed 1299 m/s | A periodic wave travels at speed v = 1299 m/s with frequency f = 9934 Hz. The wavelength is λ = v / f = 0.1308 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. |
4,162 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1416e+04 Hz, speed 868.5 m/s | A periodic wave travels at speed v = 868.5 m/s with frequency f = 1.1416e+04 Hz. The wavelength is λ = v / f = 0.07608 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. |
4,163 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 7055 Hz, speed 1042 m/s | A periodic wave travels at speed v = 1042 m/s with frequency f = 7055 Hz. The wavelength is λ = v / f = 0.1477 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. |
4,164 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1183e+04 Hz, speed 465.4 m/s | A periodic wave travels at speed v = 465.4 m/s with frequency f = 1.1183e+04 Hz. The wavelength is λ = v / f = 0.04162 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. |
4,165 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1362 Hz, speed 813 m/s | A periodic wave travels at speed v = 813 m/s with frequency f = 1362 Hz. The wavelength is λ = v / f = 0.597 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. |
4,166 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 7535 Hz, speed 385 m/s | A periodic wave travels at speed v = 385 m/s with frequency f = 7535 Hz. The wavelength is λ = v / f = 0.0511 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. |
4,167 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1581 Hz, speed 1239 m/s | A periodic wave travels at speed v = 1239 m/s with frequency f = 1581 Hz. The wavelength is λ = v / f = 0.7834 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. |
4,168 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5979 Hz, speed 441.5 m/s | A periodic wave travels at speed v = 441.5 m/s with frequency f = 5979 Hz. The wavelength is λ = v / f = 0.07385 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. |
4,169 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 4627 Hz, speed 1022 m/s | A periodic wave travels at speed v = 1022 m/s with frequency f = 4627 Hz. The wavelength is λ = v / f = 0.2208 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. |
4,170 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 6632 Hz, speed 568.8 m/s | A periodic wave travels at speed v = 568.8 m/s with frequency f = 6632 Hz. The wavelength is λ = v / f = 0.08577 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. |
4,171 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.8814e+04 Hz, speed 1407 m/s | A periodic wave travels at speed v = 1407 m/s with frequency f = 1.8814e+04 Hz. The wavelength is λ = v / f = 0.07477 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. |
4,172 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5043 Hz, speed 1144 m/s | A periodic wave travels at speed v = 1144 m/s with frequency f = 5043 Hz. The wavelength is λ = v / f = 0.2269 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. |
4,173 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1378 Hz, speed 1346 m/s | A periodic wave travels at speed v = 1346 m/s with frequency f = 1378 Hz. The wavelength is λ = v / f = 0.9768 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. |
4,174 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9363e+04 Hz, speed 389.7 m/s | A periodic wave travels at speed v = 389.7 m/s with frequency f = 1.9363e+04 Hz. The wavelength is λ = v / f = 0.02013 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. |
4,175 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1516e+04 Hz, speed 1324 m/s | A periodic wave travels at speed v = 1324 m/s with frequency f = 1.1516e+04 Hz. The wavelength is λ = v / f = 0.115 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. |
4,176 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.8638e+04 Hz, speed 900.1 m/s | A periodic wave travels at speed v = 900.1 m/s with frequency f = 1.8638e+04 Hz. The wavelength is λ = v / f = 0.04829 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. |
4,177 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 7996 Hz, speed 368 m/s | A periodic wave travels at speed v = 368 m/s with frequency f = 7996 Hz. The wavelength is λ = v / f = 0.04602 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. |
4,178 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3956e+04 Hz, speed 433 m/s | A periodic wave travels at speed v = 433 m/s with frequency f = 1.3956e+04 Hz. The wavelength is λ = v / f = 0.03103 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. |
4,179 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9430 Hz, speed 1401 m/s | A periodic wave travels at speed v = 1401 m/s with frequency f = 9430 Hz. The wavelength is λ = v / f = 0.1486 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. |
4,180 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5276 Hz, speed 336 m/s | A periodic wave travels at speed v = 336 m/s with frequency f = 5276 Hz. The wavelength is λ = v / f = 0.06368 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. |
4,181 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 6774 Hz, speed 613.1 m/s | A periodic wave travels at speed v = 613.1 m/s with frequency f = 6774 Hz. The wavelength is λ = v / f = 0.0905 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. |
4,182 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 6704 Hz, speed 1218 m/s | A periodic wave travels at speed v = 1218 m/s with frequency f = 6704 Hz. The wavelength is λ = v / f = 0.1816 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. |
4,183 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 2803 Hz, speed 956.5 m/s | A periodic wave travels at speed v = 956.5 m/s with frequency f = 2803 Hz. The wavelength is λ = v / f = 0.3412 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. |
4,184 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4683e+04 Hz, speed 1409 m/s | A periodic wave travels at speed v = 1409 m/s with frequency f = 1.4683e+04 Hz. The wavelength is λ = v / f = 0.09596 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. |
4,185 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3273e+04 Hz, speed 1354 m/s | A periodic wave travels at speed v = 1354 m/s with frequency f = 1.3273e+04 Hz. The wavelength is λ = v / f = 0.102 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. |
4,186 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 4728 Hz, speed 387.5 m/s | A periodic wave travels at speed v = 387.5 m/s with frequency f = 4728 Hz. The wavelength is λ = v / f = 0.08196 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. |
4,187 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.8961e+04 Hz, speed 1385 m/s | A periodic wave travels at speed v = 1385 m/s with frequency f = 1.8961e+04 Hz. The wavelength is λ = v / f = 0.07305 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. |
4,188 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4068e+04 Hz, speed 1219 m/s | A periodic wave travels at speed v = 1219 m/s with frequency f = 1.4068e+04 Hz. The wavelength is λ = v / f = 0.08663 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. |
4,189 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 726.5 Hz, speed 1477 m/s | A periodic wave travels at speed v = 1477 m/s with frequency f = 726.5 Hz. The wavelength is λ = v / f = 2.033 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. |
4,190 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1875 J, W = 157 J | A thermodynamic system exchanges heat Q = 1875 J with its surroundings and performs work W = 157 J. By the first law, the change in internal energy is ΔU = Q − W = 1718 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. |
4,191 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1031 J, W = -671.1 J | A thermodynamic system exchanges heat Q = 1031 J with its surroundings and performs work W = -671.1 J. By the first law, the change in internal energy is ΔU = Q − W = 1702 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. |
4,192 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 878.6 J, W = 714.6 J | A thermodynamic system exchanges heat Q = 878.6 J with its surroundings and performs work W = 714.6 J. By the first law, the change in internal energy is ΔU = Q − W = 164 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. |
4,193 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 176.3 J, W = -733.2 J | A thermodynamic system exchanges heat Q = 176.3 J with its surroundings and performs work W = -733.2 J. By the first law, the change in internal energy is ΔU = Q − W = 909.5 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. |
4,194 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -411 J, W = 12.17 J | A thermodynamic system exchanges heat Q = -411 J with its surroundings and performs work W = 12.17 J. By the first law, the change in internal energy is ΔU = Q − W = -423.2 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. |
4,195 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1126 J, W = -109.6 J | A thermodynamic system exchanges heat Q = 1126 J with its surroundings and performs work W = -109.6 J. By the first law, the change in internal energy is ΔU = Q − W = 1235 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. |
4,196 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 258.5 J, W = 559.7 J | A thermodynamic system exchanges heat Q = 258.5 J with its surroundings and performs work W = 559.7 J. By the first law, the change in internal energy is ΔU = Q − W = -301.2 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. |
4,197 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1929 J, W = -765.7 J | A thermodynamic system exchanges heat Q = 1929 J with its surroundings and performs work W = -765.7 J. By the first law, the change in internal energy is ΔU = Q − W = 2694 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. |
4,198 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = -361.6 J, W = 437.8 J | A thermodynamic system exchanges heat Q = -361.6 J with its surroundings and performs work W = 437.8 J. By the first law, the change in internal energy is ΔU = Q − W = -799.4 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. |
4,199 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1528 J, W = 54.7 J | A thermodynamic system exchanges heat Q = 1528 J with its surroundings and performs work W = 54.7 J. By the first law, the change in internal energy is ΔU = Q − W = 1474 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. |
4,200 | physics | thermodynamics | first_law | 6 | worked_example | First law of thermodynamics: Q = 1651 J, W = 291.1 J | A thermodynamic system exchanges heat Q = 1651 J with its surroundings and performs work W = 291.1 J. By the first law, the change in internal energy is ΔU = Q − W = 1360 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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