When an ideal gas at pressure, , temperature, and volume, , is isothermally compressed to , its pres — Thermodynamics and Thermochemistry Chemistry Question
Question
When an ideal gas at pressure, $P$, temperature, $T$ and volume, $V$, is isothermally compressed to $V/n$, its pressure becomes $P_i$. If the gas is compressed adiabatically to $V/n$, its pressure becomes $P_a$. The ratio of $P_i / P_a$ is
Answer: D
💡 Solution & Explanation
Isothermal: $P_i (V/n) = PV \implies P_i = nP$. Adiabatic: $P_a (V/n)^\gamma = PV^\gamma \implies P_a = n^\gamma P$. Ratio $P_i / P_a = nP / (n^\gamma P) = n^{1-\gamma}$.
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