Question

The figure here shows four paths on a p-V diagrams along which as gas can be taken from state i to state f. Rank the paths according to -

1.the change $\Delta E_{int}$ in the internal energy of the gas.

• A. 1 > 2 > 3 > 4
• B. 4 > 3 > 2 > 1
• C. 1 = 2 = 3 = 4
• D. Need more information

Answer 1

The correct option is C

1 = 2 = 3 = 4

Eint is directly proportional only to temperature and does not depend on any other variable.
Since pV = nRT, for a given pressure and volume there exists only one value of $E_{int}$.
Sinceall processes (1, 2, 3 and 4) have the same initial and final states, their initial and final $E_{int}$ will be the same.
Hence the change in $E_{int}$ for all four processes will be the same.
Since $E_{int}$ is a path-independent property of a gas, it is called an intrinsic property, or a state variable.