Question

In adiabatic irreversible expansion of an ideal gas against a constant external pressure $P_2,$ the P - V work is given by ?

• A. $-W_{irr}=nR(T_2-\frac{T_1{P}_2}{P_1})$
• B. $-W_{irr}=nR(T_2+\frac{T_1{P}_2}{P_1})$
• C. $-W_{irr}=nR{T}_1(1-\frac{P_2}{P_1})$
• D. $-W_{irr}=nR{T}_2(1-\frac{P_2}{P_1})$

Answer 1

The correct option is A

$-W_{irr}=nR(T_2-\frac{T_1{P}_2}{P_1})$

$C_v$ for diatomic ideal gas $=\frac{3}{2}RT+R=\frac{5}{2}Rmo{l}^{-1}$
$C_P$ for diatomic gas $=C_v+R=\frac{5}{2}R+R=\frac{7}{2}Rmo{l}^{-1}$
Enthalpy increase of 2 moles $=\frac{7}{2}R\times 2=7R$