The relation between internal energy U, pressure p and volume V of a gas in an adiabatic process is `U=2a+bpV`
where a and b are constants. What is the effective value of adiabatic constant `gamma`?

Options

A. `(2b+1)/(2b)`
B. `(b+1)/(b)`
C. `(b^(2)+1)/(b^(2))`
D. `((b+1)/(b))^(2)`

Answer

B

Explanation

For an adiabatic process
`0=dU+pdV`
`d(2a+bpV)+pdV=0`
`bpdV+bVdp+pdV=0`
`(b+a)pdV+bVdp=0`
`(b+1)(dV)/(V)+b(dp)/(p)=0`
`(b+1)`logp=constant
`V^(b+1)p^(b)=`constant
`pV^((b+1)/(b))=`constant
`impliesgamma=(b+1)/(b)`