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11.Thermodynamics
normal
A monoatomic gas at a pressure $P$, having a volume $V$ expands isothermally to a volume $4V$ and then adibatically to volume $16\, V$. The final pressure of the gas is (Take $\gamma = \frac{3}{2}$)
A
$32\, P$
B
$\frac{P}{{32}}$
C
$\frac{P}{{64}}$
D
$64\,P$
Solution
Isothermall process
$\mathrm{P}_{1} \mathrm{V}_{1}=\mathrm{P}_{2} \mathrm{V}_{2}$
$\mathrm{P} \times \mathrm{V}=\mathrm{P}_{2}(4 \mathrm{V})$
$\mathrm{P}_{2}=\mathrm{P} / 4$
For adiabatic process
$\frac{P}{4}(4 V)^{\gamma}=P_{f}(16 V)^{\gamma}$
$P_{f}=\frac{P}{4}\left(\frac{1}{4}\right)^{3 / 2}=\frac{P}{4} \times \frac{1}{8}=\frac{P}{32}$
Standard 11
Physics
