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 a constant pressure is :

Question

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 a constant pressure is : (A) (7/5)Q (B) (3/2)Q (C) (5/3)Q (D) (2/3)Q

Tardigrade Admin · Accepted Answer

Q = nCv Δ T Q' =nCp Δ T ∴ (Q'/Q) = (Cp/Cv) For diatomic gas: (Cp/Cv) =&gamma; = (7/5) Q' = (7/5) Q

Q. 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 a constant pressure is :

$\frac{7}{5} Q$

$\frac{3}{2} Q$

$\frac{5}{3} Q$

$\frac{2}{3} Q$

$Q = n C_{v} Δ T$
$Q^{'} = n C_{p} Δ T$
$∴ \frac{Q ^{'}}{Q} = \frac{C _{p}}{C _{v}}$
For diatomic gas : $\frac{C _{p}}{C _{v}} = γ = \frac{7}{5}$
$Q^{'} = \frac{7}{5} Q$

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

57​Q

23​Q

35​Q

32​Q