One mole of an ideal monoatomic gas undergoes a process described by the equation `PV^3` = constant. The heat capacity of the gas during this process is ……..

Options

A. 2R
B. R
C. `3/2`R
D. `5/2`R

Answer

B

Explanation

`PV^r` =constant (Polytropic process)
Heat capacity according to polytropic process formula,
`[C=C_V+R/(1-x)]`
`rArr` Comparing `PV^3`= constant with `PV^x` = constant
x=3
and for monoatomic gas f=3
`therefore C_V=(fR)/2`
Now `C=C_V+R/(1-x)`
`therefore C=(fR)/2 + R/(1-x)`
`=(3R)/2+R/(1-3) [because f=3, x=3]`
`=(3R)/2-R/2`
`therefore` C=R