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 slowly compressed to a volume V₀ / 2 and subsequently suddenly compressed to V₀ / 4 . Determine the final pressure of the gas.
Options
- A4 p₀
- B2^ + 1 p₀
- C2^ 2 p₀
- D2^ p₀
Correct answer
B. 2^ + 1 p₀
Step-by-step solution
The gas is slowly compressed while permitted to exchange heat with its surroundings, which indicates an isothermal process. For an isothermal process, the equation of state is p₁ V₁ = p₀ V₀ . Given V₁ = V₀ 2 , the pressure after the first compression is: p₁ = p₀ ( V₀ V₀ / 2 ) = 2 p₀ The gas is then suddenly compressed, which indicates an adiabatic process. For an adiabatic process, the equation of state is p₂ V₂^ = p₁ V₁^ . Given V₂ = V₀ 4 , the final pressure is: p₂ = p₁ ( V₁ V₂ )^ Substituting the values of p₁ ,