First slide

Different type of processes

Question

In an adiabatic process wherein pressure is increased by $\frac{2}{3} % if \frac{C_{p}}{C_{v}} = \frac{3}{2}$ , then the volume decreases by about:

Moderate

A

$\frac{4}{9} %$
B

$\frac{2}{3} %$
C

4%
D

$\frac{9}{4} %$

Solution

For an adiabatic process, ${PV}^{γ} = K$
Here, $γ = \frac{3}{2} and K = constant$
${PV}^{\frac{3}{2}} = K$
log P + $\frac{3}{2} \log V = o \log K$
$∴ \frac{∆ P}{P} + \frac{3}{2} \frac{∆ V}{V} = 0$
$∴ \frac{∆ V}{V} = - \frac{2}{3} \frac{∆ P}{P}$
$\frac{∆ V}{V} \times 100 = - (\frac{2}{3}) (\frac{∆ P}{P} \times 100) % = - \frac{2}{3} \times \frac{2}{3} % = - \frac{4}{9} %$
$∴ Volume decreases by about \frac{4}{9} % .$

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