When heat Q is supplied to a diatomic gas of rigid molecules at constant volume its temperature increases by $\Delta T$. The heat required to produce the same change in temperature, at constant pressure is

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Heat & Thermodynamics

When heat Q is supplied to a diatomic gas of rigid molecules at constant volume its temperature increases by

Δ T

. The heat required to produce the same change in temperature, at constant pressure is

(A) $\frac{3}{2} Q$
(B) $\frac{5}{3} Q$
(C) $\frac{7}{5} Q$ ✓ Correct
(D) $\frac{2}{3} Q$

Answer: (C)

Solution

A rigid diatomic molecule has

C_{V} = \frac{5}{2} R

and

C_{P} = \frac{7}{2} R

. At constant volume the supplied heat is

Q = n C_{V} Δ T

, whereas producing the same rise

Δ T

at constant pressure needs

Q^{'} = n C_{P} Δ T

. The ratio of the two is just the ratio of the molar heats,

\frac{Q ^{'}}{Q} = \frac{C _{P}}{C _{V}} = \frac{7/2}{5/2} = \frac{7}{5}

, so

Q^{'} = \frac{7}{5} Q

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option

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