Molar specific heat at constant volume for an ideal gas is given by `C_(v)=a+bT` (a and b are constant), `T` is temperature in Kelvin, then equation for adiabatic process is (`R`is universal gas constant)

Options

A. `T^(a)e^(bT)V^(R)`=constant
B. `T^(R)e^(bT)V^(R)`=constant
C. `T^(b)e^(aT)V^(R)`=constant
D. `T^(a)e^(R)V^(bT)`=constant

Answer

A

Explanation

For adiabatic process `DeltaQ=0`
Therefore `DeltaU=DeltaWimpliesNc_(v)dt=-PdV`
`n(a+bT)=-(nRT)/(V)dV ((a)/(T)+b) dT=-(dV)/(V)`
Integrating both sides we get `T^(a)e^(bT)V_(R)`= constant