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

Answer

A

Explanation

U = a+b PV…………(1)
`dU = -dW = (nR)/(gamma -1) (T_(2)-T_(1)) = (nR)/(gamma -1) (dT)`
`rArr U = int dU =(nR)/(gamma -1) int dT`
or `U= (nR)/(gamma -1) T + a = (PV)/(gamma -1) + a`……… (2)
where a is the constant of integration. Comparing (1) and (2), we get
`b=1/(gamma -1) rArr gamma =(b+1)/b`