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$dQ=n.Cp.\mathrm{\Delta }T$ where $$C_p={\displaystyle \frac{7}{2}}R$$ for diatomic gases. Put the value of Work done $=nR\mathrm{\Delta }T=10J$ 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) =${\displaystyle \frac{7}{2}}$R
So, $C_p={\displaystyle \frac{7}{2}}R$ ----- (1)
It is given that work done during expansion at constant pressure is dw$$=10J=n\times R\times \mathrm{\Delta }T$$------ (2)
Now, at constant pressure Heat absorbed by gas is given by
$$dQ=n.R.\mathrm{\Delta }T$$------ (3)
Putting (1) in (3)
$dQ=n.\left({\displaystyle \frac{7}{2}}R\right)\mathrm{\Delta }T$ ----------- (4)
Putting (2) in (4),
$dQ={\displaystyle \frac{7}{2}}(10)=35J$

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 ($${\text{C}}_{\text{p}}$$).