Question

The average degree of freedom per molecule for a gas is $6$. The gas performs $25\,J$ of work when it expands at constant pressure. The heat absorbed by the gas is

• A. 75 J
• B. 100 J
• C. 150 J
• D. 125 J

Answer 1

Answer: (B)

100 J

Answer 2

$\gamma = 1 + \frac{2}{f} = 1 + \frac{2}{6} = \frac{4}{3}$
$\frac{\Delta W}{\Delta Q}=\frac{\Delta Q - \Delta U}{\Delta Q} = 1-\frac{nC_{V} \Delta T}{nC_{P} \Delta T}$
$= 1 - \frac{1}{\gamma} = 1 -\frac{3}{4} =\frac{1}{4}$
$\therefore \:\: \Delta Q = 4 \Delta W = 100 J$
$\left( \because \frac{C_{P}}{C_{V}} = \gamma\right)$