Question

A sample of ideal gas ($\gamma$ = $1.4$) is heated at constant pressure. If $140J$ of heat is supplied to gas, find $\Delta U$ and $w$.

• A. 60 J, -80 J
• B. 50 J, -60 J
• C. -50 J, 60 J
• D. None of these

Answer 1

The correct option is A

60 J, -80 J

Do you remember $\gamma$ value for a diatomic gas?

$\gamma =1.4$

$\Rightarrow$ $\frac{C_P}{C_V}=1.4\Rightarrow C_P=1.4C_V$

We know that $C_P-C_V=R$; $1.4C_V-C_V=R$

$0.4C_V=R$

$\therefore C_V=\frac{5}{2}R$ & $C_P-C_V=R$; $C_P-\frac{5}{2}R=R$

$\therefore C_P=\frac{7}{2}R$

Now, $\Delta H=Q_P=n{C}_P\Delta T$

$\Delta T=\frac{\Delta }{n{C}_p}=\frac{140\times 2}{7n\times R}=\frac{40}{n}$

$w=-nR\Delta T=-n\times 2\times \frac{40}{n}=-80J$

$\therefore$ $w=-80J$

Also

$Q_P=\Delta H=\Delta U+(-w)$

$\Delta U=\Delta H+w$

$\Delta U=140-80$

$\therefore \Delta U=60J$

Also

$Q_P=\Delta H=\Delta U+(-w)$

$\Delta U=\Delta H+w$

$\Delta U=140-80$

$\therefore$$\Delta U=60J$