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

Three identical adiabatic containers A , B , and C hold helium, neon, and oxygen respectively at equal pressures. These gases are compressed to half their original volumes. Which of the following statements are correct?

Options

  1. AThe final temperatures in the three containers will be identical.
  2. BThe final pressures in the three containers will be identical.
  3. CThe temperatures of helium and neon will be identical, whereas that of oxygen will differ.
  4. DThe pressures of helium and neon will be identical, whereas that of oxygen will differ.

Correct answer

D. The pressures of helium and neon will be identical, whereas that of oxygen will differ.

Step-by-step solution

For an adiabatic process, the pressure and volume are related by PV^ = constant , and temperature and volume are related by TV^ -1 = constant . Let the initial pressure, volume, and temperature of the gases be P₀ , V₀ , and T₀ respectively. The final volume is V = V₀ 2 . The final pressure is given by P = P₀ ( V₀ V )^ = P₀ (2)^ . The final temperature is given by T = T₀ ( V₀ V )^ -1 = T₀ (2)^ -1 . Helium and neon are monoatomic gases, so their ratio of specific heats is = 5 3 . Oxygen is a diatomic gas, so its rati

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