MCQ
The volume of air increases by $5\%$ in its adiabatic expansion. The percentage decrease in its pressure will be ...... $\%$
- A$5$
- B$6$
- ✓$7$
- D$8$
✓
Answer
Correct option: C.
$7$
c
(c) $P{V^\gamma } = K$or $P\gamma \,{V^{\gamma - 1}}dV + dP.\;{V^\gamma } = 0$
or $\frac{{dP}}{P} = - \gamma \frac{{dV}}{V}$ or $\frac{{dP}}{P} \times 100 = - \gamma \,\left( {\frac{{dV}}{V} \times 100} \right)$
$ = - 1.4 \times 5 = 7\% $
(c) $P{V^\gamma } = K$or $P\gamma \,{V^{\gamma - 1}}dV + dP.\;{V^\gamma } = 0$
or $\frac{{dP}}{P} = - \gamma \frac{{dV}}{V}$ or $\frac{{dP}}{P} \times 100 = - \gamma \,\left( {\frac{{dV}}{V} \times 100} \right)$
$ = - 1.4 \times 5 = 7\% $
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