ThermodynamicsHard
Question
When an ideal gas at pressure P, temperature T and volume, V, is isothermally compressed to V/n, its pressure becomes Pi. If the gas is compressed adiabatically to V/n, its pressure becomes Pa. The ratio of Pi /Pa is
Options
A.1
B.n
C.$n^{\gamma}$
D.$n^{(1 - \gamma)}$
Solution
Isothermal: $P.V = P_{i} \times \frac{V}{n} \Rightarrow P_{i} = n.P$
Adiabatic: $P.V^{\gamma} = P_{a} \times \left( \frac{V}{n} \right)^{\gamma} \Rightarrow P_{a} = n^{\gamma}.P$
$\therefore\frac{P_{i}}{P_{a}} = \frac{n.P}{n^{\gamma}.P} = n^{1 - \gamma}$
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