Question

A diatomic gas with rigid molecules does 10J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process?
A) ${\text{35J}}$
B) ${\text{40J}}$
C) ${\text{25J}}$
D) ${\text{30J}}$

Answer 1

The heat absorbed by gas is given by$dQ = n.Cp.\Delta T$ where ${C_p} = \dfrac{7}{2}R$ for diatomic gases. Put the value of Work done $= nR\Delta T = 10J$ in the equation of $dQ$ and obtain heat absorbed.

Complete step by step answer:
As it is given that gas in diatomic, we understand that Cp (specific heat of gas at constant pressure) =$\dfrac{7}{2}$R
So, ${C_p} = \dfrac{7}{2}R$ ----- (1)
It is given that work done during expansion at constant pressure is dw$= 10J = \;n \times R \times \Delta T$------ (2)
Now, at constant pressure Heat absorbed by gas is given by
$dQ = n.R.\Delta T$------ (3)
Putting (1) in (3)
$dQ = n.\left( {\dfrac{7}{2}R} \right)\Delta T$ ----------- (4)
Putting (2) in (4),
$dQ = \dfrac{7}{2}(10) = 35J$

So, the correct answer is “Option C”.

Note: When pressure is kept constant, heat supplied will partially increase its internal energy (temp.) and partially will be utilized in performing work against external pressure. Therefore, in case of ${{\text{C}}_{\text{p}}}$, more heat will be required to increase temperature of gas through $1^\circ C.$
A gas has two specific heats. One is defined as specific heat of gas at constant volume (${{\text{C}}_{\text{v}}}$) and other is defined as specific heat of gas at constant pressure (${{\text{C}}_{\text{p}}}$).