Question

A gas undergoes change in its state from position $A$ to position $B$ via three different paths as shown. Select the correct alternatives:

• A. Change in internal energy in all the three paths is equal.
• B. In all the three paths heat is absorbed by the gas.
• C. Heat absorbed by the gas is maximum in path (1).
• D. Temperature of the gas first increases and then decreases continuously in path (1).

Answer 1

Answer: (A), (B), (C)

Heat absorbed by the gas is maximum in path (1).

Internal energy $\left(U\right)$ depends oniy on the initial and final states. Hence, $\Delta U$ will be same in all the three paths.

In all the three paths, work done by the gas is positive and the product $PV$ or temperature $T$ is increasing. Therefore, internal energy is also increasing. So, from the first law of thermodynamics, heat will be absorbed by the gas.

Further, area under $P-V$ graph is maximum in path $1$, while $\Delta U$ is same for all the three paths. Therefore, heat absorbed by the gas is maximum in path $1$.

For temperature of the gas, we can see that product $PV$ first increases in path $1$ but whether it is decreasing or increasing later on we cannot say anything about it unless the exact values are known to us.