An ideal gas whose adiabatic exponent `gamma` is expanded according to the law `P=alphaV`, where `alpha` isa constant the initial volume of the gas is equal to `V_(@)`. As a result of expansion, the volume increases 4 times. Select the correct option for above information.

Options

A. Molar heat capacity of gas in the process is `(R(gamma+1))/(2(gamma-1))`
B. Work done by the gas is `15V_(o)^(2)(alpha)/2`
C. Change in internal energy of gas is `15V_(o)^(2)(alpha)/2`
D. Both `B` and `C` are correct

Answer

A, B

Explanation

A. `P=alphaV`
`PV^(-1)=alpha`
We know for polytropic process
`PV^(x)=` constant
`:.x=-1`
We know `C=C_(v)-R/(x-1)`
`C=C_(v)+R/2`
`C=R/(gamma-1)+R/2`
`C=(R(gamma+1))/(2(gamma-1))`
B. `dW=-PdV`
`dW=-alpha VdV`
On integrating above equation. ltbgt `W=-alpha[((4V_(o))^(2))/2-(V_(o)^(2))/2]`
`W=-(alpha)/2[16V_(o)^(2)-V_(0)^(2)]`
`W=-15V_(o)^(2) (alpha)/2`