Question

There are two identical containers \(C_1\) and \(C_2\) containing identical gases. Gas in \(C_1\) is reduced to half of its original volume adiabatically, while the gas in container \(C_2\) is also reduced to half of its initial volume isothermally. Find the ratio of final pressure in these containers. \(\gamma\) be the adiabatic constant)

• A. 2:1
• B. 1:2
• C. \(2^{\gamma - 1}:1\)
• D. \(2^{\gamma}:1\)

Hint:

For adiabatic processes, remember \(P V^{\gamma} = \text{constant}\), and for isothermal, \(P V = \text{constant}\).

Answer 1

The Correct Option is D

For adiabatic processes: \[ P_1 V_1^{\gamma} = P_2 V_2^{\gamma} \] For an isothermal process, \(P_1 V_1 = P_2 V_2\). Since the volume is halved in both processes, the change in pressure in the adiabatic process will follow the law \(P_2 = P_1 (2^{\gamma})\). Hence, the ratio of final pressures is \(2^{\gamma}:1\). \bigskip