Question

5 mol of gas at 5 atm pressure contained in a 100L cylinder absorbed 30.26 kJ of heat when it expanded to 200L at 2atm pressure. The change in internal energy of gas is:

Answer 1

For case $1$

$PV=nRT$

$T=\frac{PV}{nR}=\frac{5\times 100}{5\times 0.0821}=1218K$

For case $2$

$T=\frac{PV}{nR}=\frac{2\times 200}{5\times 0.0821}=974.42K$

Now, change in internal energy

$\Delta u=q-\Delta p\Delta v$

$=30.26-\left[\right(2-5\left)\right(200-100\left)\right]/1000$

$=30.56kJ$