Question

A certain mass of gas is expanded from (1L, 10 atm) to (4L, 5 atm) against a constant external pressure of 1 atm. If initial temperature of gas is 300K and the heat capacity of process is $50J{/}^{\circ }C$. Then the enthalpy change during the process is:
(1L atm = 100 J)

• A. $\Delta H=15kJ$
• B. $\Delta H=15.7kJ$
• C. $\Delta H=14.3kJ$
• D. $\Delta H=14.7kJ$

Answer 1

The correct option is B $\Delta H=15.7kJ$

For the state 1,
PV=nRT
$\therefore 1\times 10=n\left(0.0821\right)\left(300\right)$
$\therefore n=0.4$
For state 2,
$4\times 5=0.4\times \left(0.0821\right)\left(T_2\right)$
$T_2=600K$
$\Delta U=q+W$
$=50\left(\Delta T\right)+(-P_{ex})\left(\Delta V\right)$
$=50\left(300\right)J-\left(1atm\right)\left(3L\right)$
$=15000-300$
$\therefore \Delta U=14700J$
$\Delta H=\Delta U+\Delta \left(PV\right)$
$=14700J+(5\times 4-10)atmL$
$=15700$
$\Delta H=15.7kJ$