Topic 2.4: Thermodynamics (HL) Questions

An ideal gas is heated so that it expands at constant pressure 2.5 × 10⁵ Pa, its volume rising from 1.6 × 10⁻³ m³ to 3.2 × 10⁻³ m³. What is the work done by the gas?

An ideal gas is taken once around a closed thermodynamic cycle, returning to its initial state. What is the change in its internal energy over the complete cycle?

120 J of heat is removed from a gas while the surroundings do 70 J of work compressing it. What is the change in the internal energy of the gas?

A heat engine rejects 480 J of heat to its cold reservoir each cycle while doing 320 J of useful work. What is its efficiency?

A mass releases 5460 J of heat as it solidifies at a constant temperature of 273 K. What is the change in entropy of this mass?

Which statement correctly describes a spontaneous (unaided) process in an isolated system?

An ideal gas is taken once around a closed cycle on a p–V diagram, returning to its starting state. What is the net change in the internal energy of the gas over the complete cycle?

An engine works between a hot reservoir at 600 K and a cold reservoir at 240 K. What is the maximum possible efficiency of the engine?

A gas absorbs 250 J of heat and at the same time does 90 J of work as it expands. What is the change in the internal energy of the gas?

During an adiabatic compression of an ideal gas, 250 J of work is done on the gas. What is the change in the internal energy of the gas?

A fixed mass of ideal gas is heated while its volume is held constant. Which statement about the energy transfers is correct?

A gas is heated at a constant pressure of 5.0×10⁴ Pa and its volume increases by 6.0×10⁻³ m³. How much work does the gas do?

A sealed rigid container holds a fixed mass of gas. The container cannot change shape, so the gas keeps a constant volume while 450 J of heat is supplied to it.

(a) State the work done by the gas, and justify your answer.
(b) Determine the change in the internal energy of the gas.

A gas in a piston is heated at a constant pressure of 1.2×10⁵ Pa. Its volume increases from 5.0×10⁻³ m³ to 9.0×10⁻³ m³, and during the heating 1500 J of heat is supplied.

(a) Determine the work done by the gas.
(b) Hence determine the change in the internal energy of the gas.

A mass of 0.40 kg of water at its freezing point of 273 K is cooled until it has completely frozen into ice, releasing heat to its surroundings. The specific latent heat of fusion of water is 3.3 × 10⁵ J kg⁻¹.

Calculate the change in entropy of the water as it freezes.

An ideal gas is compressed suddenly and quickly inside a well-insulated cylinder, so that no heat can enter or leave during the compression. During the compression 480 J of work is done on the gas.

(a) State the name of this type of process.
(b) Determine the change in the internal energy of the gas, and state whether its temperature rises or falls.

When the water in the previous part freezes, its entropy decreases. A student claims this breaks the second law of thermodynamics.

Outline why the freezing of the water is in fact consistent with the second law.

Outline why a cyclic process, in which a gas is taken around a closed loop on a p–V diagram and returns to its starting state, is able to operate as a heat engine that does useful work each cycle.

A fixed mass of ideal gas is taken once around a closed cycle on a p–V diagram, returning to its starting state.

(a) State the net change in the internal energy of the gas over the complete cycle.
(b) During the cycle the gas absorbs 3200 J of heat in total and rejects 2300 J of heat in total. Determine the net work done by the gas over the cycle.

A series of small heat pulses ΔQ is added to a reservoir held at a fixed temperature, and the resulting entropy change ΔS of the reservoir is recorded. The data lie on a straight line through the origin:

ΔQ / J : 200, 400, 600, 800
ΔS / J K⁻¹ : 0.50, 1.00, 1.50, 2.00

(a) Determine the gradient of a graph of ΔS against ΔQ.
(b) Hence determine the temperature of the reservoir.