WORK DONE IN ADIABATIC PROCESS

Options

A. `(nR(T_1-T_2))/gamma`
B. `(nR(T_1-T_2))/(gamma-1)`
C. `n gamma(T_1-T_2)R`
D. `(gamma(T_1-T_2)R)/n`

Answer

B

Explanation

`W=int_(V_1)^(V_2)PdV=K int_(V_1)^(V_2)(dV)/(V^gamma)`
`K[V^(-gamma+1)/(-gamma+1)]_(V_1)^(V_2)`
`=K/(1-gamma)[1/(V_2^(gamma-1))-1/(V_1^(gamma-1))]`
`W=1/(1-gamma)[(P_2V_1^gamma)/(V_2^(gamma-1))-(P_1V_1^gamma)/(V_1^(gamma-1))]`
`=1/(1-gamma)[P_2V_2-P_1V_2]`
`=(nR)/(1-gamma)(T_2-T_1)=(nR(T_1-T_2))/((gamma-1))`
`[ :. P_1V_1=nRT_1 and P_2V_2=nRT_2]`