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
$=\frac{U_1-U_2}{U_1}=\frac{n{C}_v\left(T_1-T_2\right)}{n{C}_v{T}_1}$
$=1-\frac{T_2}{T_1}=1-\frac{273+27}{273+927}$
$=1-\frac{300}{1200}$
$=1-\frac{1}{4}=\frac{3}{4}=0.75$