Question

In an adiabatic process, the work done by the gas is 500 J. What is the change in internal energy of the gas?

• A. 0 J
• B. +500 J
• C. –500 J
• D. Cannot be determined

Hint:

In adiabatic processes, the system does work at the expense of its internal energy, since \( Q = 0 \). Thus, \( \Delta U = -W \).

Answer 1

The Correct Option is C

Step 1: Use the First Law of Thermodynamics.
\[ \Delta U = Q - W \] where:
\( \Delta U \) is the change in internal energy,
\( Q \) is the heat added to the system,
\( W \) is the work done by the system.
Step 2: Use the condition for an adiabatic process.
In an adiabatic process, no heat is exchanged: \[ Q = 0 \] Thus, the equation becomes: \[ \Delta U = 0 - W = -W \] Step 3: Substitute the given value.
Work done by the gas is \( W = 500 \, \text{J} \), so: \[ \Delta U = -500 \, \text{J} \] Therefore, the internal energy of the gas decreases by 500 J.