Question

Figure shows two processes A and B on a system. Let ∆Q₁ and ∆Q₂ be the heat given to the system in processes A and B respectively. Then
(a) ∆Q₁ > ∆Q₂ (b) ∆Q₁ = ∆Q₂ (c) ∆Q₁ < ∆Q₂ (d) ∆Q₁ ≤ ∆Q₂.

Answer 1

(a) ∆Q₁ > ∆Q₂

Both the processes A and B have common initial and final points. So, change in internal energy, ∆U is same in both the cases. Internal energy is a state function that does not depend on the path followed.

In the P-V diagram, the area under the curve represents the work done on the system, ∆W. Since area under curve A > area under curve B, ∆W_​1> ∆W₂.
Now,
$$\begin{gathered} \Delta Q_1=\Delta U+\Delta W_1 \\ \Delta Q_2=\Delta U+\Delta W_2 \\ \mathrm{But}\Delta W_1>\Delta W_2 \\ \Rightarrow \Delta Q_1>\Delta Q_2 \end{gathered}$$

Here, ∆Q₁ and ∆Q₂ denote the heat given to the system in processes A and B, respectively.