Question

A gas undergoes the change in its state from position A to position B via three different paths as shown in figure. Select the correct alternative (s).
(1) temperature of the gas first increases and then decreases continuously in path $1$
(2) heat absorbed/released by the gas is maximum in path $1$
(3) change in internal energy in all the three paths is equal
(4) in all the three paths heat is absorbed by the gas

• A. 1, 2 and 3 are correct
• B. 1 and 2 are correct
• C. 2 and 4 are correct
• D. 1 and 3 are correct

Answer 1

Answer: (A)

Internal energy $(U)$ depends only 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 (volume is increasing) and the product $p V$ or temperature $T$ is increasing. Therefore, internal energy is also increasing so, from 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 three paths. Therefore, heat absorbed by the gas is maximum in path $1$ . For temperature of the gas we can see the product $p v$ which first increases in paht $1$ and then decreases us.