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COMEDK2023Evening ShiftPhysicsThermodynamicsActual

If the ratio of specific heat of a gas at constant pressure to that at constant volume is , the change in internal energy of a mass of a gas when the volume changes from V to 3 ~V at constant pressure is

Options

  1. A2 P V
  2. BR ( -1)
  3. C2 P V ( -1)
  4. D2 P V

Correct answer

C. 2 P V ( -1)

Step-by-step solution

The change in internal energy U for an ideal gas is given by the formula U = n C_ v T . For an ideal gas, C_ v = R - 1 . Thus, U = n ( R - 1 ) T . Using the ideal gas law PV = nRT , at constant pressure P , we have P V = nR T . Substituting nR T = P V into the expression for internal energy, we get U = P V - 1 . Given the volume changes from V to 3V , the change in volume is V = 3V - V = 2V . Therefore, U = P(2V) - 1 = 2PV - 1 . Answer: 2 P V ( -1)

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