A monatomic ideal gas is following the cyclic proces ABCA. Then choose the incorrect option.

Options

A. molar heat capacity for the process AB is `R/2`
B. Heat is rejected by the system in path BC.
C. Molar heat capacity for the process BC is `(2)/(3)R`
D. Work done by the system in the process CA is `(2U_(0))/(3)ln4`

Answer

C

Explanation

For path AB
TV = constant
`rArr PV^(2)`=constant
For polytropic process `PV^(m)`=constant
On comparing eqn (i) and (ii)
m=2
The molar heat capacity is geven as
`C=(R )/(gamma-1)-(R )/(m-1)`, for monatiomic `gamma=(5)/(3)`
`C=(3R)/(2)-R=(R)/(2)`
`C=((R/5)/(3)-1)-(R )/(2-1)=(3)/(2)R-R=(R )/(2)`
so option (a) is correct .
For BC it is an isochoric process and temperature is decreaseing so option (b) is correct.
`C=C_(V)=(3)/(2)R`, so option (c )is wrong.
For process CA (isothermal)
`W=nRTln(V_(A)/(V_(C )))`
`W=(2)/(3)/(2)nRT)ln(4)`
`=(2)/(3)U_(0)ln(4)`
So, option (d) is correct.