Question

We consider a thermodynamic system. If \(\Delta U\) is the increase in internal energy and \(W\) is the work done by the system, which one of the following statement is true?

• A. \(\Delta U=-W\) in an adiabatic process
• B. \(\Delta U=W\) in an isothermal process
• C. \(\Delta U=-W\) in an isothermal process
• D. \(\Delta U=W\) in an adiabatic process

Hint:

Apply the first law, heat equals change in internal energy plus work done by the system, and check what is zero in each process.

Answer 1

The Correct Option is A

Step 1: Write the First Law
$\Delta Q=\Delta U+W$.

Step 2: Check Each Process
Adiabatic: $\Delta Q=0\Rightarrow\Delta U=-W$.
Isothermal: $\Delta U=0$.

Step 3: Eliminate
The options with $\Delta U=W$ or $\Delta U=\pm W$ for isothermal fail because $\Delta U=0$ there. Only the adiabatic $\Delta U=-W$ remains.

Final Answer:
Only delta U equals minus W for an adiabatic process is correct. \[ \boxed{\text{(A) }\Delta U=-W\ \text{in an adiabatic process}} \]