Question

Five moles of an ideal gas at $300K$, expanded isothermally from an initial pressure of $4atm$ to a final pressure of 1 atm against a cont. external the pressure of $1atm$. Calculate $q,w,$ $\Delta U$ & $\Delta H$. Calculate the corresponding value of all if the above process is carried out reversibly

• A. $w_{irr}=9356.25J,w_{rev}=17291.6J,\Delta U=\Delta H=0$
• B. $w_{irr}=-9356.25J,w_{rev}=17291.6J,\Delta U=\Delta H=0$
• C. $w_{irr}=9356.25J,w_{rev}=-17291.6J,\Delta U=\Delta H=0$
• D. None of these

Answer 1

Answer: (A)

$w_{irr}=9356.25J,w_{rev}=17291.6J,\Delta U=\Delta H=0$

$W_{irr}=-nRT(1-\frac{P_2}{P_1})=-5\times 8.314\times 300(1-\frac{1}{4})$
$W_{irr}=-9.353kJ$
$W_{rev}=-2.303nRTlog\left(\frac{V_2}{V_1}\right)$
$W_{rev}=2.303\times 5\times 8.314\times 300log4$
$W_{rev}=17.29kJ$
and $\Delta q=\Delta EW$
at $\Delta T\to 0\Delta E\to 0\Delta H\to 0$
$W_{rev}=q=17.29kJ$