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

Hint: 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 (\[{{\text{C}}_{\text{p}}}\]).