First slide

Different type of processes

Question

One mole of an ideal monoatomic gas undergoes a process described by the equation $p v^{3} = c o n s \tan t$ constant. The heat capacity of the gas during this process is

Easy

A

$\frac{3}{2} R$
B

$\frac{5}{2} R$
C

2R
D

R

Solution

Process described by the equation, $P V^{3} = C o n s \tan t$ For a polytropic process, $P V^{α} = c o n s \tan t$
$C = C_{V} + \frac{R}{1 - α} = \frac{3}{2} R + \frac{R}{1 - 3} = R (∵ α = 3)$

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