Thermodynamics - Result Question 15
16. A monoatomic gas at a pressure $P$, having a volume $V$ expands isothermally to a volume $2 V$ and then adiabatically to a volume $16 V$. The final pressure of the gas is : $(.$ take $.\gamma=\frac{5}{3})$
[2014]
(a) $64 P$
(b) $32 P$
(c) $\frac{P}{64}$
(d) $16 P$
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Answer:
Correct Answer: 16. (c)
Solution:
- (c) For isothermal process $P_1 V_1=P_2 V_2$
$\Rightarrow PV=P_2(2 V) \Rightarrow P_2=\frac{P}{2}$
For adiabatic process
$ \begin{aligned} & P_2 V_2^{\gamma}=P_3 V_3^{\gamma} \\ & .\Rightarrow \quad(\frac{P}{2})(2 v)^{\gamma}=P_3 16 v)^{\gamma} \\ & \Rightarrow \quad P_3=\frac{3}{2}(\frac{1}{8})^{5 / 3}=\frac{P}{64} \end{aligned} $
