Question

Pick out the INCORRECT STATEMENT

• A. Internal energy of an ideal gas depends only on its temperature
• B. Change in the internal energy in a cyclic process is not zero
• C. Change in the internal energy of a gas depends only on its initial and final states
• D. Internal energy depends upon state of matter
• E. Change in the internal energy in a cyclic process is zero

Hint:

State functions depend only on initial and final states.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question tests fundamental concepts of thermodynamics, particularly the properties of internal energy (U). Internal energy is a state function, which means its value depends only on the current state of the system, not on the path taken to reach that state.
Step 2: Detailed Explanation:
Let's analyze each statement:
(A) Internal energy of an ideal gas depends only on its temperature: This is a correct statement, a key property of ideal gases. The internal energy is the sum of the kinetic energies of the molecules, which is directly proportional to the absolute temperature (\(U \propto T\)).
(C) Change in the internal energy of a gas depends only on its initial and final states: This is the definition of a state function. Internal energy is a state function, so this statement is correct. The change \(\Delta U = U_{final} - U_{initial}\) is independent of the process path.
(D) Internal energy depends upon state of matter: This is correct. The internal energy of a substance in its solid, liquid, or gaseous state will be different, even at the same temperature, due to differences in potential energy between molecules.
(E) Change in the internal energy in a cyclic process is zero: A cyclic process is one where the system returns to its initial state. Since internal energy is a state function, if the initial and final states are the same, the change in internal energy must be zero (\(\Delta U = U_{final} - U_{initial} = 0\)). This statement is correct.
(B) Change in the internal energy in a cyclic process is not zero: This statement directly contradicts statement (E) and the fact that internal energy is a state function. Therefore, this statement is incorrect.
Step 3: Final Answer:
The incorrect statement is "Change in the internal energy in a cyclic process is not zero".