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One mole of an ideal monatomic gas undergoes a process described by the equation $PV^3$ = constant. The heat capacity of the gas during this process is
A
2 R
B
R
C
$\frac{3}{2}R$
D
$\frac{5}{2}R$
Explanation
$C = C_V + R/(1 - x)$.
Detailed Solution
$PV^x$ = constant (polytropic process); heat capacity $C = C_V + \frac{R}{1 - x}$
Given x = 3 and the gas is monatomic (f = 3)
$C = \frac{fR}{2} + \frac{R}{1 - x} = \frac{3}{2}R - \frac{R}{2} = R$
Given x = 3 and the gas is monatomic (f = 3)
$C = \frac{fR}{2} + \frac{R}{1 - x} = \frac{3}{2}R - \frac{R}{2} = R$