Question

Five moles of an ideal gas at 293 K is expanded isothermally from an initial pressure of 2.1 MPa to 1.3 MPa against at constant external pressure 4.3 MPa. The heat transferred in this process is _____ $kJmo{l}^{-1}$.
(Rounded-off to the nearest integer)

[$R=8.314Jmo{l}^{-1}{K}^{-1}$]

Answer 1

For isothermal expansion at constant pressure, heat gained by the system is given by

$Q=-W$ ($\Delta U=0$)
$W=-P\Delta V$
$Q=+P_{ex}(V_2-V_1)$

$V_2=\frac{nRT}{P_2}$
$V_1=\frac{nRT}{P_1}$
$Q=P_{ex}\times n\times R\times T(\frac{1}{P_2}-\frac{1}{P_1})$
$=4.3\times 5\times 8.314\times 293[\frac{1}{1.3}-\frac{1}{2.1}]$

$=15.345kJmo{l}^{-1}$
Heat transferred per mole is :
$q=\frac{15.345}{5}=3.06\approx 3kJ/mol$