If a monoatomic gas undergoes a thermodynamic proces for which its molar heat capacity is equal to the universal gas constant. What is the process in terms of `V` and `T` ?

Options

A. `VT^-(1//2)=` constant
B. `VT^(1//2)=` constant
C. `V^(2)T^(2)=` constant
D. `VT=` constant

Explanation

`C=R`
`(dQ)/(ndT)=R`
`rArr(nC_(v)dT+dW)/(ndT)=RrArrCv+(pdV)/(ndT)=RrArr(pdV)/(ndT)=-(R )/(2)`[ `:'C_(v)=3R//2`]
`rArr(RT)/(V)(dV)/(dT)=-(R )/(2)`[`(P)/(n)=(RT)/(v)`]
`rArr (dV)/(V)=(dT)/(2T)rArrln(VT^(1//2))=` constant
`rArr VT^(1//2)=` constant