MCQ
A gas at $NTP$ is suddenly compressed to one-fourth of its original volume. If $\gamma $ is supposed to be $\frac{3}{2}$, then the final pressure is........ atmosphere
- A$4$
- B$1.5$
- ✓$8$
- D$0.25$
✓
Answer
Correct option: C.
$8$
c
(c) $P{V^\gamma } = {\rm{constant}} \Rightarrow \frac{{{P_2}}}{{{P_1}}} = {\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^\gamma }$$ \Rightarrow \frac{{{P_2}}}{1} = {\left( {\frac{{{V_1}}}{{{V_1}/4}}} \right)^{3/2}} = 8$
==> ${P_2} = 8\;atm$.
(c) $P{V^\gamma } = {\rm{constant}} \Rightarrow \frac{{{P_2}}}{{{P_1}}} = {\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^\gamma }$$ \Rightarrow \frac{{{P_2}}}{1} = {\left( {\frac{{{V_1}}}{{{V_1}/4}}} \right)^{3/2}} = 8$
==> ${P_2} = 8\;atm$.
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