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Exam
NEET
Subject
Physics
Chapter
Kinetic Theory of Gases

NEET · Physics · Kinetic Theory of Gases

One mole of an ideal diatomic gas undergoes a process as shown in...

One mole of an ideal diatomic gas undergoes a process as shown in the figure. The molar specific heat of the gas in the process is
One mole of an ideal diatomic gas undergoes a process as shown in the figure. The molar specific heat of the gas in the

Options

  1. A3R/23 R / 2
  2. BR/2R / 2
  3. C5R/25 R / 2
  4. D7R/27 R / 2

Correct answer

A. 3R/23 R / 2

Step-by-step solution

In the curve, V∝1TV \propto \frac{1}{T}⇒V=m1T where, m= slope of  curve. &⇒VT= constant &∴TdV+VdT=0&⇒dV=−VTdT& As, Q=ΔU+W&CdT=CVdT+pdV&CdT=CVdT−pTVdT&⇒C=CV−pVT&=CV−R(∵pVT=R)&\begin{aligned}& \Rightarrow V=m \frac{1}{T} \text{ where, } m=\text{ slope\text{ of } curve. } \& \Rightarrow V T=\text{ constant } \& \therefore \quad T d V+V d T=0 \& \Rightarrow \quad d V=-\frac{V}{T} d T \& \text{ As, } Q=\Delta U+W \& C d T=C_V d T+p d V \& C d T=C_V d T-\frac{p}{T} V d T \& \Rightarrow \quad C=C_V-\frac{p V}{T} \& =C_V-R \quad\left(\because \frac{p V}{T}=R\right) \&\end{aligned}$Fordiatomicgas,For diatomic gas,C_V=\frac{5}{2} R \therefore \quad C=C_V-R=\frac{5}{2} R-R=\frac{3 R}{2}$
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