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11.Thermodynamics
normal
$2$ moles of a diatomic gas undergoes the process : $PT_2/V$ = constant. Then, the molar heat capacity of the gas during the process will be equal to
A
$5R/2$
B
$9R/2$
C
$3R$
D
$4R$
Solution
$: \rightarrow$ Given hrocess is
$\frac{P T^2}{V} =\text { constant }$
$C_v =\frac{5}{2} R \quad \text { For }$
$C_V=\frac{5}{2} R \text { (For diatomic }\text { equation } \text { gas) }$
(We know the gas equation gas)
$P V =n R T$
$\therefore T \propto P V$
$\frac{P P^2 V^2}{V} =\text { constant }$
$P^3 V =k$
$P V^{1 / 3} =\text { constant }-\text { (1) }$
formula for molar heat cahacity
$C =C_v+\frac{R}{1-x}$
$x =1 / 3 \text { from eq (1) }$
$\therefore \quad C =\frac{S}{2} R+\frac{R}{1-\frac{1}{3}}$
$C =4 R$
Standard 11
Physics