Compression of Gas in Two Containers – Rankers Physics

Thermodynamics: Practice Problem & Solution

Consider two containers A and B containing identical gases at the same pressure, volume and temperature. The gas in container A is compressed to half of its original volume isothermally while the gas in container B is compressed to half of its original value adiabatically. The ratio of final pressure of gas in B to that of gas in A is:
\(2^{\gamma - 1}\)
\(\left(\frac{1}{2}\right)^{\gamma - 1}\)
\(\left(\frac{1}{1 - \gamma}\right)^2\)
\(\left(\frac{1}{\gamma - 1}\right)^2\)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Thermodynamics. Understanding the underlying formula is key to arriving at the correct answer below:

For isothermal process in A: \(P_A = 2P_0\). For adiabatic process in B: \(P_B = P_0 (2)^\gamma\). The ratio of final pressures is \(\frac{P_B}{P_A} = \frac{P_0 2^\gamma}{2 P_0} = 2^{\gamma - 1}\).

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