Question

A thermodynamic system is changed from state \( (P_1, V_1) \) to \( (P_2, V_2) \) by two different processes, the quantity which will remain same will be –

• A. \( \Delta Q \)
• B. \( \Delta W \)
• C. \( \Delta Q + \Delta W \)
• D. \( \Delta Q - \Delta W \)

Hint:

The change in internal energy of a system is path-independent and remains the same for two different processes between the same initial and final states.

Answer 1

The Correct Option is D

Step 1: Understand the first law of thermodynamics.
The first law states that \( \Delta Q = \Delta W + \Delta U \), where \( \Delta Q \) is the heat added to the system, \( \Delta W \) is the work done, and \( \Delta U \) is the change in internal energy.
Step 2: Conclusion.
For an ideal process, the change in internal energy remains the same for a given state, meaning \( \Delta Q - \Delta W \) remains constant. Final Answer: \[ \boxed{\Delta Q - \Delta W} \]