The molar specific heat of a gas is defined as `C=(Dq)/(ndT)` Where `dQ`=heat absorbed
`n` = mole number `dT` = change in temperature
The equation of the above process in the variables `T ,V` is

Options

A. `TV^(gamma-1)`=constant
B. `TV^(((gamma-1)/(2)))`=constant
C. `TV^(((gamma)/(gamma-1)))`=constant
D. `TV^(((gamma-1)/(gamma)))`=constant

Answer

B

Explanation

`C=(R)/(gamma-1)+p(dV)/(dT)`
`=(R)/(gamma-1)+alphaV.(R)/(2alphaV)=(R)/(gamma-1)+(R)/(2)=(R(gamma+1))/(2(gamma-1))`
`Q=-DeltaU=DeltaU+W , or W=-2DeltaU`
`C=(R)/(gamma-1)+((-2RdT)/((gamma-1)dT))=(R)/(1-gamma)`
`pdV=(-2RdT)/(gamma-1)`
`(RT)/(V)dV=(-2)/(gamma-1)RdT(dT)/(T)=-((gamma-1))/(2)(dV)/(V)`
log `T=-((gamma-1))/(2)logV =logV^(-(gamma-1)/(2))+logK`
or log `TV^((gamma-1)/(2))=` constant