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

Phase 1: Apply the First Law of Thermodynamics.
\[\Delta U = Q - W\]Variables:
\( \Delta U \) represents the internal energy change,
\( Q \) is the heat input to the system,
\( W \) is the work output from the system.
Phase 2: Implement the adiabatic process condition.
An adiabatic process involves zero heat transfer:\[Q = 0\]Consequently, the equation simplifies to:\[\Delta U = 0 - W = -W\]Phase 3: Insert the provided numerical value.
Given that the work performed by the gas is \( W = 500 \, \text{J} \), we have:\[\Delta U = -500 \, \text{J}\]Conclusion: The internal energy of the gas decreases by 500 J.