First law of thermodynamics (A-level only) — AQA A-Level Physics

The first law of thermodynamics is a fundamental principle in A-level Physics that extends the concept of energy conservation to thermal systems. It relates the change in internal energy of a system to the heat transferred to or from the system and the work done on or by the system. This law is essential for understanding how energy is transferred and transformed in processes ranging from car engines to biological systems.

In the AQA A-level specification, this topic is part of the thermal physics section and is examined through calculations and explanations of thermodynamic processes. It builds on prior knowledge of energy transfer, work, and the kinetic theory of gases, and it provides a foundation for more advanced topics such as entropy and the second law of thermodynamics. Mastery of this law is crucial for analysing real-world applications and for achieving high marks in exam questions that require both quantitative and qualitative reasoning.

• →Internal energy is the sum of the random kinetic and potential energies of the particles in a system, and for an ideal gas, it depends only on temperature.
• →The first law of thermodynamics: delta U = Q + W, where delta U is the change in internal energy, Q is the heat supplied to the system, and W is the work done on the system.
• →Sign convention: Q is positive when heat is supplied to the system, negative when lost; W is positive when work is done on the system (compression), negative when work is done by the system (expansion).
• →Work done on or by a gas at constant pressure is given by W = -p delta V, where p is the external pressure and delta V is the change in volume.
• →For an ideal gas, an isothermal process has delta U = 0, so Q = -W; an adiabatic process has Q = 0, so delta U = W.

• States the first law as Q = ∆U + W and identifies each symbol with its meaning and sign convention.
• Applies the equation to a numerical problem, substituting Q, ∆U and W with correct signs and solving for the unknown.
• Explains that ∆U is the increase in internal energy and that for an ideal gas it is directly proportional to the change in thermodynamic temperature.
• Distinguishes between work done by the system (positive W) and work done on the system (negative W), and between heating to the system (positive Q) and cooling (negative Q).
• Uses the law to deduce energy changes in a cyclic process, where ∆U = 0 over a complete cycle so Q = W.
• Applies Q = ∆U + W to an isothermal process, stating ∆U = 0 and hence Q = W.
• Applies Q = ∆U + W to an adiabatic process, stating Q = 0 and hence ∆U = −W, linking work done on a gas to a temperature rise.
• Applies Q = ∆U + W to a constant-volume (isochoric) process, stating W = 0 and hence Q = ∆U.
• Explains a cyclic process by stating that ∆U = 0 over a complete cycle, so the net heating equals the net work done by the system.
• Uses the first law to explain a practical example, such as a bicycle pump warming when air is compressed quickly or a gas canister cooling as it discharges.

• 💡Always write the sign convention next to the equation before substituting numbers, so the examiner can see your reasoning.
• 💡When a gas expands, W is positive; when it is compressed, W is negative. Check this before calculating.
• 💡For a cyclic process, state that ∆U = 0 and therefore Q = W, which often simplifies the calculation.
• 💡Identify the process type first (isothermal, adiabatic, isochoric, cyclic) and write the resulting simplification before calculating.
• 💡For adiabatic processes, state clearly that Q = 0 and link the sign of W to whether the gas is compressed or expands.
• 💡When explaining a practical example, name the process and justify the simplification using the first law.
• 💡Always write down the first law equation and define your sign convention before substituting values. This shows the examiner you understand the physics and helps avoid sign errors.
• 💡When explaining processes, refer to the first law explicitly. For example, for an adiabatic expansion, state that Q = 0, so delta U = W, and since W is negative, delta U is negative, leading to a temperature decrease.
• 💡For calculation questions, ensure units are consistent (e.g., convert cm^3 to m^3 for volume) and always include the correct sign for Q and W. Marks are often awarded for correct substitution and final answer with units.

• Using the wrong sign for work done on the system: the error is treating work done on the gas as positive W; the correction is to use W = −(work done on the gas) because W is work done by the system.
• Forgetting that ∆U is an increase, not a final value: the error is substituting the final internal energy instead of the change; the correction is to calculate ∆U = U_final − U_initial.
• Mixing up Q and W in rearrangement: the error is writing ∆U = Q + W when work is done by the system; the correction is to use ∆U = Q − W for work done by the system.
• Assuming Q = 0 for any rapid process: the error is treating a fast process as automatically adiabatic; the correction is to check whether the process is thermally insulated or whether heating has time to occur.
• Forgetting that ∆U = 0 for an isothermal process only for an ideal gas: the error is applying ∆U = 0 to a real gas isothermal process; the correction is to state the ideal-gas assumption.
• Confusing constant-volume with constant-pressure processes: the error is setting W = 0 for a process that expands at constant pressure; the correction is to use W = 0 only when volume is constant.
• Students often think that internal energy is the same as temperature. Correction: Internal energy is the total kinetic and potential energy of particles, while temperature is a measure of the average kinetic energy per particle. For an ideal gas, internal energy is directly proportional to temperature, but for real substances, potential energy also contributes.
• Students may believe that if a gas expands, it always cools down. Correction: A gas cools during an adiabatic expansion (no heat exchange), but if heat is supplied during expansion, the temperature may remain constant (isothermal) or even increase.
• Students sometimes confuse the sign of work done. Correction: In the equation delta U = Q + W, W is positive when work is done on the gas (compression) and negative when the gas does work (expansion). Always check the direction of energy transfer.

1. 1Day 1-2: Review the definition of internal energy and the first law equation. Learn the sign conventions for heat and work, and practice identifying them in different scenarios.
2. 2Day 3-4: Study the application of the first law to isothermal, adiabatic, isobaric, and isochoric processes. Create a table summarising the values of Q, W, and delta U for each process for an ideal gas.
3. 3Day 5-6: Work through calculation problems involving the first law, including those with changes in volume, pressure, and temperature. Pay attention to unit conversions and sign conventions.
4. 4Day 7-8: Practice exam-style questions, especially those that require explanations of real-world applications, such as a bicycle pump heating up or a gas expanding in a cylinder. Focus on using precise terminology.
5. 5Day 9-10: Complete a past paper section on thermal physics, marking your answers against the mark scheme. Review any mistakes and revisit the relevant concepts.

• 📋Calculation of change in internal energy: Given values of heat supplied and work done, or a scenario where you must determine work from pressure and volume change. Advice: Always write the equation, substitute with signs, and state the final answer with units.
• 📋Explanation of a thermodynamic process: Describe what happens to the internal energy, heat, and work in a given process (e.g., adiabatic expansion). Advice: Use the first law explicitly and refer to the sign convention.
• 📋Graph analysis: Interpret a pressure-volume graph to determine work done (area under the curve) and relate it to internal energy changes. Advice: Remember that work done on the gas is the negative of the area under the curve if the gas expands.
• 📋Practical application: Explain the physics of a real-world device, such as a heat pump or a car engine, using the first law. Advice: Link the processes to the equation and discuss energy transfers.