Question

A monoatomic gas $ (\gamma =5/3) $ at pressure P is suddenly compressed to $ \frac{1}{8} $ th of its volume adiabatically, the pressure of gas is :

• A. $ \frac{43}{3}P $
• B. $ 8P $
• C. $ 32\,P $
• D. $ \frac{24}{5}P $

Answer 1

Answer: (C)

The condition that must be obeyed by an ideal gas in an adiabatic process is given by
$P V^{\gamma}=$ constant
or $P_{1} V_{1}^{\gamma}=p_{2} V_{2} \gamma$
or $P_{2}=P_{1}\left(\frac{V_{1}}{V_{2}}\right)^{\gamma}$
Here, $P_{1}=P, \frac{V_{2}}{V_{1}}=\frac{1}{8}, \gamma=\frac{5}{3}$
$\therefore P_{2}=P(8)^{5 / 3}$
or $P_{2}=P\left(2^{3}\right)^{5 / 3}=32 P$
Note: The equation $P V^{\gamma}=$ constant can be written in terms of other pair of thermodynamic variables by combining it with the ideal gas law $(P V=n R T)$. In doing so, we will find that, $T V^{\gamma-1}=$ constant and $T^{\gamma} P^{1-\gamma}=$ constant.