First slide

Different type of processes

Question

Heat is supplied to a diatomic gas at constant pressure. The ratio of ΔQ : ΔU : ΔW is:

Easy

A

5:3:2
B

5:2:3
C

7:5:2
D

7:2:5

Solution

At constant pressure, ΔQ = nC_pΔT
ΔU = nC_vΔT
By 1st law of thermodynamics, ΔQ = ΔU + W
$\therefore W = \Delta Q - \Delta U = n\left( {{C_p} - {C_v}} \right)\Delta T = nR\Delta T$
Also, ${C_v} = \frac{R}{{\gamma - 1}},\,\,{C_p} = \frac{{\gamma R}}{{\gamma - 1}}$
For diatomic gas, $\gamma = 1 + \frac{2}{5} = \frac{7}{5}$
$\therefore \Delta Q:\Delta U:\Delta W$
$= {C_p}:{C_v}:R = \frac{{\gamma R}}{{\gamma - 1}}:\frac{R}{{\gamma - 1}}:R$
$= \gamma :1:\left( {\gamma - 1} \right) = \frac{7}{5}:1:\frac{2}{5} = 7:5:2$

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