Question

Figure shows two processes $A\text{and}B$ on a system. Let $\Delta Q_1\text{and}\Delta Q_2$ be the heat given to the system in processes $A\text{and}B$ respectively. Then

• A. $\Delta Q_1>\Delta Q_2$
• B. $\Delta Q_1=\Delta Q_2$
• C. $\Delta Q_1<\Delta Q_2$
• D. $\Delta Q_1\le \Delta Q_2$

Answer 1

Answer: (A)

$\Delta Q_1>\Delta Q_2$

Both the process $A$ and $B$ have common initial and final points. So, change in internal energy, $\Delta U$ 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, $\Delta W$. since area under curve $A$ > area under curve $B$, $\Delta W_1>\Delta W_2$.

Now,

$\Delta Q_1=\Delta U+\Delta W_1$

$\Delta Q_2=\Delta U+\Delta W_1$

But $\Delta W_1>\Delta W_2$

$\Rightarrow \Delta Q_1>\Delta Q_2$

Here, $\Delta Q_1$ and $\Delta Q_2$ denote the heat given to the system in processes $A$ and $B$, Respectively.