Question

The fractional change in internal energy when a gas is cooled from $ 927{}^\circ C $ to $ 27{}^\circ C $ is

• A. 0.25
• B. 0.75
• C. 1
• D. 0.67

Answer 1

Answer: (B)

Initial internal energy,
$U_{1}=n C_{v} T_{1}^{o}$
Final internal energy,
$U_{2}=n C_{\nu} T_{2}$
$\therefore $ Fractional change
$=\frac{U_{1}-U_{2}}{U_{1}}=\frac{n C_{v}\left(T_{1}-T_{2}\right)}{n C_{v} T_{1}} $
$=1-\frac{T_{2}}{T_{1}}=1-\frac{273+27}{273+927}$
$=1-\frac{300}{1200}$
$=1-\frac{1}{4}=\frac{3}{4}=0.75$