Thermal Physics: Practice Problem & Solution
13. A monoatomic gas at a pressure $P$, having a volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is (take $\gamma = 5/3$): (2014)
Solution Explained:
To solve this problem, we apply the core principles of Thermal Physics. Understanding the underlying formula is key to arriving at the correct answer below:
For isothermal process $P_1V_1 = P_2V_2 \Rightarrow P \times V = P_2 \times 2V \Rightarrow P_2 = P/2$. For adiabatic process $P_2V_2^{\gamma} = P_3V_3^{\gamma} \Rightarrow (P/2)(2V)^{5/3} = P_3(16V)^{5/3} \Rightarrow P_3 = P/64$.
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