The average degrees 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

Q: The average degrees 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

Ans: (b)

Sol: f = 6

$\gamma = 1 + \frac{2}{\gamma} $

$\gamma = 1 + \frac{2}{6} = \frac{4}{3} $

$C_p = \frac{\gamma R}{\gamma -1} $

$\large C_p = \frac{\frac{4}{3} R}{\frac{4}{3} -1} $

C_p = 4 R

∆W = n R ∆T

∆Q_p = n C_p ∆T

$\large \frac{\Delta W}{\Delta Q_p} = \frac{R}{C_p} = \frac{1}{4}$

∆Q_p = 4 ∆W = 4 × 25 = 100 J