Questions: First Law of Thermodynamics

Question 1

An ideal gas undergoes isothermal expansion (temperature stays constant). Which statement correctly describes what happens?

• A. The gas does no work because its temperature does not change
• B. No heat flows because internal energy is a state function
• C. The gas does positive work and an equal quantity of heat flows in
• D. Both heat and work are zero since ΔU = 0

Answer: (C)

For an ideal gas, internal energy depends only on temperature. At constant T, ΔU = 0. From the First Law: ΔU = Q − W gives 0 = Q − W, so Q = W. The gas expands (positive work done by the gas, W > 0), and heat must flow in from the surroundings (Q > 0) to supply that energy. Options A and D incorrectly conclude work or heat are zero from ΔU = 0 — a direct target of the most common misconception.

Question 2

Heat and internal energy are essentially the same thing — heat is just the name for the energy stored inside a system.

• T. True
• F. False

Answer: False

Internal energy (U) is a state function — a property of the system's current thermodynamic state (temperature, pressure, volume). Heat (Q) is an energy transfer process, not a stored quantity. A system does not 'contain heat'; it contains internal energy. Heat describes energy crossing the boundary during a process. Conflating them is a foundational error: you can have Q = 0 with large ΔU (adiabatic work), or ΔU = 0 with large Q (isothermal expansion).

Question 3

A gas is compressed adiabatically (Q = 0). What happens to its internal energy, and why? Use the First Law explicitly.

Model answer: Internal energy increases. With Q = 0, the First Law gives ΔU = Q − W = 0 − W = −W. Compression means work is done ON the gas, so W < 0 by the system-centric sign convention (the system does negative work). Therefore ΔU = −W > 0: the internal energy — and thus the temperature — rises.

This is why a bicycle pump gets warm and why diesel engines ignite fuel by compression alone: adiabatic compression converts mechanical work entirely into internal energy. The sign convention is critical here — W is work done BY the system, so compression (work done ON the system) is W < 0.