Question

In a process, \(\Delta U=0\) and \(q\neq 0\). Then the process must involve

• A. No work is done during the process.
• B. Heat is transferred, but no mechanical work occurs.
• C. Work done by or on a system exactly equal in magnitude and opposite in sign to a heat transfer.
• D. There is a change in internal energy of the system throughout the process.

Hint:

Apply the first law, delta U = q + w, with delta U equal to zero.

Answer 1

The Correct Option is C

Step 1: Rearrange
$\Delta U=0$ gives $q=-w$.

Step 2: Meaning
Any heat absorbed is fully converted to work by the system, or work done on the system leaves as heat.

Step 3: Select
Only option (C) states this.

Final Answer:
The work and heat are equal and opposite. \[ \boxed{\text{(C) }\text{Work done equals heat transfer in magnitude, with opposite sign}} \]