The molar heat capacity of a monoatomic ideal gas undergoing the process PV1 / 2=constant is

Question

The molar heat capacity of a monoatomic ideal gas undergoing the process PV1 / 2=constant is (A) (15/2)R (B) (23/2)R (C) (7/2)R (D) Zero

Tardigrade Admin · Accepted Answer

For a polytropic process, specific heat of an ideal gas is given by, c=(R/&gamma; - 1)+(R/1 - n) [n = (1/2) , f o r t h i s p o l y t r o p i c p r o c e s s] c=(R/(5)3 - 1)+2R =(3 R/2)+2R=(7 R/2)

Q. The molar heat capacity of a monoatomic ideal gas undergoing the process $P V^{1/2} = co n s t an t$ is

$\frac{15}{2} R$

$\frac{23}{2} R$

$\frac{7}{2} R$

Zero

For a polytropic process, specific heat of an ideal gas is given by,
$c = \frac{R}{γ - 1} + \frac{R}{1 - n} [n = \frac{1}{2}, f or t hi s p o l y t ro p i c p rocess]$
$c = \frac{R}{\frac{5}{3} - 1} + 2 R$
$= \frac{3 R}{2} + 2 R = \frac{7 R}{2}$

Q. The molar heat capacity of a monoatomic ideal gas undergoing the process PV1/2=constant is

215​R

223​R

27​R