A gas is heated at constant pressure. The fraction of heat absorbed used in doing work is — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

At constant pressure, q_p = n * $C_p$ * dT, and work done BY the gas is W = P * dV = n * R * dT. The fraction used in doing work is W / q_p = n*R*dT / (n*$C_p$*dT) = R/$C_p$. Since $C_p$ - $C_v$ = R, we have R/$C_p$ = ($C_p$ - $C_v$)/$C_p$ = 1 - $C_v$/$C_p$ = 1 - 1/γ.