First slide

Thermometry

Question

A gas is confined inside a container having a movable piston. The gas is allowed to expand isobarically. If the initial volume of gas is $V_{0}$ and the speed of sound in the gas is $C_{0}$ , then the speed of sound when the volume of the gas increases to $4 V_{0}$ is

Easy

A

$C_{0}$
B

$2 C_{0}$
C

$4 C_{0}$
D

$C_{0} / 2$

Solution

$C = \sqrt{\frac{γ R T}{M}}$
For isobaric process, $\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$
$H e n c e \frac{V_{0}}{T_{1}} = \frac{4 V_{0}}{T_{2}} \Rightarrow T_{2} = 4 T_{1}$
$F r o m \frac{C_{1}}{C_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} \Rightarrow \frac{C_{0}}{C_{2}} = \sqrt{\frac{T_{0}}{4 T_{0}}} \Rightarrow C_{2} = 2 C_{0}$

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