A full set of ten original structured questions in the style of Paper 4, covering the whole of Thermodynamics: internal energy and the first law. With only two lessons in the topic, most questions link them, taking a process and tracking both the energy transfers and the internal energy. The sign convention is ΔU = q + W, where W is the work done on the gas. Each question is linked to its lessons; attempt them all, then reveal the worked solutions.
Fig. 1.1 represents the molecules of a fixed mass of ideal gas in random motion.
(a) State what is meant by the internal energy of a system. [2]
(b) Explain why, for an ideal gas, the internal energy is entirely kinetic. [2]
(c) The temperature of the gas is raised. State and explain the effect on its internal energy. [2]
(d) State whether the internal energy of this gas depends on its pressure and volume separately or only on its temperature, and justify your answer briefly. [2]
(e) The gas is 0.50 mol of a monatomic ideal gas at 300 K. Using U = ₃⁄₂ nRT, calculate its internal energy. [3]
(f) The gas is now compressed to half its volume at constant temperature. State the change in its internal energy. [1]
A gas expands at a constant pressure of 1.5 × 10⁵ Pa, its volume increasing from 2.0 × 10⁻³ m³ to 5.0 × 10⁻³ m³. Fig. 2.1 shows this change on a p–V diagram.
(a) Show that the work done by a gas expanding at constant pressure is W = pΔV. [2]
(b) Calculate the work done by the gas in this expansion. [2]
(c) State what the work done is represented by on the p–V diagram. [1]
(d) During the expansion, 900 J of thermal energy is supplied to the gas. Use the first law to find the change in its internal energy. [3]
(e) State and explain whether the temperature of the gas rises, falls or stays the same. [2]
(f) State the sign of the work done on the gas if instead it were compressed at constant pressure. [1]
(g) The gas instead expands by the same amount with no thermal energy supplied. State and explain what happens to its temperature. [2]
A fixed mass of ideal gas is taken through several separate processes, each starting from the state S shown in Fig. 3.1.
(a) State the first law of thermodynamics in the form ΔU = q + W, defining each symbol and its sign convention. [3]
(b) The gas is heated at constant volume, gaining 600 J of thermal energy. State the work done on the gas and the change in internal energy. [2]
(c) In a separate isothermal expansion the gas does 400 J of work. State the change in internal energy and the heat transferred. [2]
(d) In a separate adiabatic compression, 250 J of work is done on the gas. State the change in internal energy and what happens to the temperature. [2]
(e) Using the first law, explain why compressing a gas rapidly raises its temperature. [2]
(f) Explain why ΔU = 0 for any process that returns the gas to its original state. [2]
This question is about the meaning of internal energy.
(a) Explain what is meant by the internal energy of a system. [2]
(b) State why the motion of the molecules is described as random. [1]
(c) For an ideal gas, state and explain which type of molecular energy contributes to the internal energy. [2]
(d) Hence explain why the internal energy of an ideal gas depends only on its temperature. [2]
(e) State what happens to the internal energy of an ideal gas if its temperature is held constant while p and V change. [1]
(f) State what happens to the internal energy of a fixed mass of ideal gas if its kelvin temperature is doubled. [2]
A real gas is compared with an ideal gas.
(a) State the two contributions to the internal energy of a substance. [2]
(b) Explain why the internal energy of an ideal gas has no potential-energy contribution. [2]
(c) A fixed mass of ideal gas is heated from 300 K to 600 K. State the ratio of its final to initial internal energy, and explain. [3]
(d) Explain why two samples of the same ideal gas at the same temperature but different volumes have the same internal energy per mole. [2]
(e) State whether the internal energy depends on the current state of the gas or on the path taken to reach it. [1]
A gas at a constant pressure of 1.5 × 10⁵ Pa expands from 2.0 × 10⁻³ m³ to 5.0 × 10⁻³ m³, as shown in Fig. 6.1.
(a) Write the expression for the work done by a gas at constant pressure. [1]
(b) Calculate the work done by the gas during the expansion. [2]
(c) State the sign of the work done on the gas, and explain. [2]
(d) State what the work done corresponds to on the p-V diagram. [1]
(e) The gas is then compressed back to 2.0 × 10⁻³ m³ at a constant pressure of 2.5 × 10⁵ Pa. Calculate the work done on the gas. [2]
(f) State the net work done on the gas over the two stages. [2]
0.050 mol of an ideal monatomic gas is heated at constant volume; 250 J of thermal energy is supplied. Parts (a) to (c) use the first law; parts (d) and (e) use internal energy.
(a) State the first law of thermodynamics, defining each symbol. [2]
(b) State the work done on the gas at constant volume, and explain. [2]
(c) Hence state the increase in internal energy. [1]
(d) Explain, in terms of the molecules, what this increase in internal energy represents. [2]
(e) State and explain what happens to the temperature of the gas. [2]
(f) If instead the gas were allowed to expand as it was heated, state whether the temperature rise would be larger or smaller for the same heat supplied. [2]
An ideal gas expands isothermally. This question links internal energy with the first law.
(a) State what happens to the internal energy of the gas, and explain. [2]
(b) Apply the first law to this process. [2]
(c) State the direction of heat flow as the gas expands isothermally. [2]
(d) The gas does 600 J of work on the surroundings. State the work done on the gas and the heat supplied. [2]
(e) Describe the isothermal expansion on a p-V diagram and state what the area under it represents. [2]
(f) Explain why the temperature is unchanged even though the gas absorbs heat. [1]
A gas is compressed rapidly so that no heat enters or leaves it (an adiabatic change).
(a) State the value of q for an adiabatic process. [1]
(b) Apply the first law to an adiabatic change. [2]
(c) The gas is compressed, so work is done on it. State and explain what happens to its internal energy and temperature. [3]
(d) 300 J of work is done on the gas. State the change in internal energy. [1]
(e) Explain, in molecular terms, why an adiabatic compression raises the temperature. [2]
(f) State and explain what happens to the temperature during an adiabatic expansion. [2]
A fixed mass of ideal gas is taken through a cycle and returns to its original state, as suggested by Fig. 10.1. This question applies the first law to the steps and uses the fact that internal energy is a function of state.
(a) In the first step (constant volume), 200 J of heat is supplied. State the work done on the gas and the change in internal energy. [2]
(b) In the second step (constant-pressure expansion), 500 J of heat is supplied and the gas does 180 J of work. Calculate the change in internal energy. [2]
(c) After the complete cycle the gas returns to its starting state. State the total change in internal energy over the cycle, and explain. [3]
(d) Over the whole cycle the net work done on the gas is +120 J. Calculate the net heat transferred, and state its direction. [3]
(e) Explain why the internal energy at the end of the second step is greater than at the start of the cycle. [2]
Mark this once you have attempted all ten questions and checked your working against the solutions. Revealing the solutions alone does not count.