The relation between U, p and V for an ideal gas in an adiabatic process is given by relation `U=a+bpV`. Find the value of adiabatic exponent `(gamma)` of this gas.

Options

A. `(a+1)/(a)`
B. `(b+1)/(b)`
C. `(b+1)/(a)`
D. `(a)/(b+1)`

Answer

B

Explanation

`U = a + bPV = a + bnRT`
`implies DeltaU = bnRDeltaT = nC_(v)DeltaT`
`implies C_(v) = bR implies C_(P) = bR + R`
` implies gamma=(C_(p))/( C_(v)) = (bR+R)/(bR) = (b+1)/(b)`