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Concepts Of Physics MCQ Edition [Volume 2]PhysicsSpecific Heat Capacities of Gases

A given mass of a gas, with a specific heat ratio C_p / C_V = , has an initial pressure p₀ and an initial volume V₀ . The gas is permitted to exchange heat with its surroundings. It is suddenly compressed from the volume V₀ to V₀ / 2 and subsequently slowly compressed to V₀ / 4 . Determine the final pressure of the gas.

Options

  1. A2^ 2 p₀
  2. B4 p₀
  3. C2^ p₀
  4. D2^ + 1 p₀

Correct answer

B. 4 p₀

Step-by-step solution

The initial state of the gas has pressure p₀ , volume V₀ , and temperature T₀ . Since the gas is permitted to exchange heat with its surroundings, the surroundings are at the initial temperature T₀ . The gas is first suddenly compressed from V₀ to V₀ 2 . This sudden process is adiabatic, causing the temperature of the gas to increase above T₀ . Subsequently, the gas is slowly compressed to a final volume of V₀ 4 . Because this process is slow and the gas can exchange heat with its surroundings, it will reach therma

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