When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

Q: When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

(a) 2/5

(b) 3/5

(c) 3/7

(d) 5/7

Ans: (d)

Sol: For diatomic gas, γ = 7/5

At constant pressure ∆Q = n C_p ∆T

∆U = n C_v ∆T (always)

$\large \frac{\Delta U}{\Delta Q} = \frac{n C_v \Delta T}{n C_p \Delta T} $

$\large \frac{\Delta U}{\Delta Q} = \frac{C_v}{C_p} $

$\large \frac{\Delta U}{\Delta Q} = \frac{1}{\gamma} = \frac{5}{7} $