Question

For adiabatic ideal gas near room temperature, what fraction of heat supplied is available for external work. If the gas is expanded at a constant pressure? At a constant temperature?

Answer 1

In the process of expansion at constant pressure p, assuming that the volume increases from $V_1$ to $V_2$ and temperature change from $T_1$ to $T_2$ , we have

$PV_1=nRT_1$

$PV_2=nRT_2$

In this process, the work done by the system on the outside world is $W = p(V_2-V_1)= nRΔT$ and increase in internal energy of the system is

$ΔU = C_vΔT$

$\frac{W}{Q}=\frac{W}{\Delta U + W}=\frac{nR}{C_v +nR}=\frac{2}{7}$