ThermodynamicsHard

Question

An ideal gas ($\gamma$ = 1.5) undergoes a change in state such that the magnitude of heat absorbed by the gas is equal to the magnitude of work done on the gas. The molar heat capacity of the gas in this process is

Options

A.2R
B.R
C.3R
D.1.5R

Solution

$q = \Delta U - w$ and from the question, $q = |w| = w$ or $2q = \Delta U$

$\text{Or }2.n.C_{m}.\Delta T = n.C_{v,m}.\Delta T \Rightarrow C_{m} = \frac{C_{v,m}}{2} = \frac{1}{2} \times \frac{R}{1.5 - 1} = R$

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