The molar heat capacity of an ideal gas in a process varies as `C=C_(V)+alphaT^(2)` (where `C_(V)` is mola heat capacity at constant volume and `alpha` is a constant). Then the equation of the process is

Options

A. `Ve^(-((alphaT^(2))/(2R)))=` Constant
B. `Ve^(-((alphaT^(2))/(R)))=` constant
C. `Ve^(-((2alphaT^(2))/(R)))=` constant
D. `Ve^(-((3alphaT^(2))/(2R)))=` constant

Answer

A

Explanation

Given
`C=C_(V)+alphaT^(2)`
`C_(V)+(RT)/(V)(dV)/(dT)=C_(V)+alphaT^(2)`
`int(alphaT)/(R)dT=int(dV)/(V)+lnk`
`(alphaT^(2))/(2R)=ln(kV)`
`kV=e^((alphaT^(2))/(2R))`
`thereforeVe^(-((alphaT^(2))/(2R)))`=constant