Looking for classes? Ksquare Career Institute, Bengaluru →
A monoatomic gas at pressure $P_1$ and volume $V_1$ is compressed adiabatically to $\frac{1}{8}$th its original volume. What is the final pressure of the gas?
A
$64P_1$
B
$P_1$
C
$16P_1$
D
$32P_1$
Detailed Solution
For an adiabatic process: $PV^\gamma$ = constant; for a monoatomic gas $\gamma = \frac{5}{3}$
$P_1V_1^{5/3} = P_2\left(\frac{V_1}{8}\right)^{5/3}$
$P_2 = P_1(8)^{5/3}$
$(8)^{5/3} = (2^3)^{5/3} = 2^5 = 32$
$P_2 = 32P_1$
$P_1V_1^{5/3} = P_2\left(\frac{V_1}{8}\right)^{5/3}$
$P_2 = P_1(8)^{5/3}$
$(8)^{5/3} = (2^3)^{5/3} = 2^5 = 32$
$P_2 = 32P_1$