Questions: First Law of Thermodynamics for Closed Systems

Question 1

A gas sealed in a rigid container (fixed volume) absorbs 300 J of heat. What is the change in internal energy?

• A. ΔU = 0 J
• B. ΔU = 300 J
• C. ΔU = -300 J
• D. Cannot be determined without knowing the pressure

Answer: (B)

In a rigid container, the volume cannot change, so no boundary work is done: W = ∫P dV = 0. Applying the first law, ΔU = Q − W = 300 − 0 = 300 J. All the heat input goes directly into raising the internal energy. Pressure data is irrelevant here because work is zero regardless of pressure when volume is fixed.

Question 2

If the same gas is compressed from state A to state B quickly (irreversibly) and then slowly (quasi-statically), the change in internal energy ΔU will be different for the two processes.

• T. True
• F. False

Answer: False

Internal energy U is a state function — it depends only on the thermodynamic state (temperature, pressure, composition), not on the path taken to reach that state. Both processes end at state B, so ΔU = U_B − U_A is identical. What differs between the two processes is the work W and heat Q exchanged with the surroundings, which must change together to keep ΔU the same.

Question 3

A piston-cylinder device contains steam that is heated while the piston moves outward. Identify Q and W in ΔU = Q − W and explain the sign of each.

Model answer: Q is positive because heat is added to the system (heat flows in). W is positive because the system does work on the surroundings as the piston expands outward (W = ∫P dV > 0 for expansion). ΔU equals Q minus W, so the internal energy increase is the net of heat added minus work done by the steam.

The sign convention ΔU = Q − W treats heat added to the system as positive and work done by the system as positive. Expansion does positive work on the surroundings, reducing internal energy relative to what heat alone would provide. If the steam expands a lot, it may do nearly as much work as the heat added, resulting in a small ΔU despite significant Q.