Question

An ideal gas undergoes a cyclic transformation starting from point A and coming back to the same point by tracing the path A→B→C→D→A as shown in the three cases below.

Choose the correct option regarding \(\Delta U\):

• A. \(\Delta U({Case-III})>\Delta U({Case-II})>\Delta U({Case-I})\)
• B. \(\Delta U({Case-I}) = \Delta U({Case-II}) = \Delta U({Case-III})\)
• C. \(\Delta U({Case-I})>\Delta U({Case-II})>\Delta U({Case-III})\)
• D. \(\Delta U({Case-I})>\Delta U({Case-III})>\Delta U({Case-II})\)

Hint:

For any cyclic process, \(\Delta U = 0\) because the system returns to the initial thermodynamic state.

Answer 1

The Correct Option is B

• For a cyclic process, the internal energy change (\(\Delta U\)) is always zero as the system returns to its initial state.
• Since \(\Delta U\) is a state function, it depends only on the initial and final states, which are the same for all three cases.