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

Hint: In this question we should know the formula of degrees of freedom and their relationship with other quantities and also about the law of equipartition of energy i.e.,
$\mathrm{\Delta }u={\displaystyle \frac{f}{2}}RT$

Formula used -
1) $\mathrm{\Delta }w=nR\mathrm{\Delta }T$
2) $\mathrm{\Delta }u={\displaystyle \frac{f}{2}}RT$

Complete step-by-step answer:
A gas molecule is not constrained in which direction it can travel, so it has three degrees of freedom of translation. This holds true for all gas molecules, whether monatomic, diatomic or polyatomic, as any molecule can travel freely in all directions in three-dimensional space.
Given, Degree of freedom=6
Work performed by gas=25 J
$$\begin{gathered} \mathrm{\Delta }u={\displaystyle \frac{f}{2}}R\mathrm{\Delta }T=3RT \\ \mathrm{\Delta }w=nR\mathrm{\Delta }T=25.5 \\ \mathrm{\Delta }Q=\mathrm{\Delta }V+\mathrm{\Delta }W \\ =3nR\mathrm{\Delta }T-nR\mathrm{\Delta }T=4nR\mathrm{\Delta }T \\ =4\times 25=100J \end{gathered}$$
Hence, the correct answer is 100 J
Hence, the correct option is B.
Temperature is held constant, therefore the change in energy is zero (U=0). So, the heat absorbed by the gas equals the work done by the ideal gas on its surroundings. Enthalpy change is also equal to zero because the change in energy zero and the pressure and volume is constant.

Note: Within a mathematical equation the degrees of freedom reflect how many values involved in an equation have the freedom to differ. A molecule which is monatomic, diatomic, and triatomic has 3, 5, and 6 degrees of freedom.