Thermodynamics

• U belongs to the state; q and W belong to the process. In ΔU = q + W, the W is work done on the gas — so expansion makes it negative.

• 16.1.1 I can understand — understand that internal energy is determined by the state of the system and that it can be expressed as the sum of a random distribution of kinetic and potential energies associated with the molecules of a system
• 16.1.2 I can relate — relate a rise in temperature of an object to an increase in its internal energy
• 16.2.1 I can recall — recall and use W = pΔV for the work done when the volume of a gas changes at constant pressure and understand the difference between the work done by the gas and the work done on the gas
• 16.2.2 I can recall — recall and use the first law of thermodynamics ΔU = q + W expressed in terms of the increase in internal energy, the heating of the system (energy transferred to the system by heating) and the work done on the system

Units, significant figures and working are part of the physics. Give a calculated answer to the same number of significant figures as the least precise data, or one more; keep full precision in the working and round only at the end; write the unit with every final answer. A fifth of the qualification is experimental: Papers 3 and 5 test AO3 only, and their questions may be set in contexts outside the syllabus content, so the practical work in this chapter is set out as method, recording, graphs and uncertainties rather than as theory.

• “When a gas expands, W in ΔU = q + W is +pΔV.” Correct W in ΔU = q + W is the work done ON the system. An expanding gas does work on its surroundings, so the work done on it is negative: W = −pΔV. Write “work done on the gas” or “work done by the gas” beside every number.
• “Internal energy is the total heat in a body.” Correct Internal energy is the sum of a random distribution of the kinetic and potential energies of the molecules. Heating is a transfer, not a store: a body has internal energy, and q is energy that crosses its boundary during a process.
• “If the internal energy increases, the temperature must rise.” Correct A temperature rise does mean U rises, but not the reverse. During melting or boiling U rises at constant temperature, because the potential energy of the molecules rises.
• “The gas is back where it started, so q = 0 for the cycle.” Correct Only ΔU = 0 round a cycle, because U is fixed by the state. q and W are transfers and need not be zero; the net q equals minus the net W.
• “W = pΔV whatever happens to the pressure.” Correct Only at constant pressure. When p changes, the work is the area under the p–V graph.
• “The gas expands by 250 cm3, so pΔV = 1.0 × 105 × 250.” Correct Convert to m3 first: 250 cm3 = 2.50 × 10−4 m3, so the work done by the gas, pΔV, is 25.0 J, and the work done on it is −25.0 J. Pa × m3 gives joules; Pa × cm3 does not.
• “Internal energy is the kinetic energy of the molecules.” Repair It is the sum of a random distribution of the kinetic and potential energies of the molecules. The potential part is what changes during melting and boiling.
• “Internal energy is the total heat in a body.” Repair Heating is a transfer, not a store. A body has internal energy; q is energy that crosses its boundary during a process.
• “A fast-moving ball has more internal energy than the same ball at rest.” Repair The ball's ordered kinetic energy is not internal energy. Only the random motion of its molecules counts, and that is set by its temperature.
• “The gas took a longer route, so its change in internal energy was bigger.” Repair ΔU depends only on the start and end states. The route changes q and W, never ΔU.
• “If internal energy increases, the temperature must rise.” Repair During a change of state U rises at constant temperature. Only the kinetic part of U is tied to temperature.
• “An ideal gas has potential energy because the molecules attract.” Repair An ideal gas has no intermolecular forces, so no potential energy: its internal energy is all kinetic and depends only on T.
• “U = (3/2)nRT for any gas.” Repair Only for a monatomic ideal gas. Molecules with two or more atoms also have rotational energy.
• “The gas expands, so W in ΔU = q + W is +pΔV.” Repair W is the work done on the gas. An expanding gas does work on its surroundings, so W = −pΔV.
• “q is the heat in the gas.” Repair q is the energy transferred to the system by heating, and it is negative if energy leaves.
• “W = pΔV, whatever happens to the pressure.” Repair Only at constant pressure. Otherwise use the area under the p–V graph.
• “Over a complete cycle q = 0, because the gas is back where it started.” Repair ΔU = 0 over a cycle. q and W need not be zero; net q = −net W, and the net work is the area enclosed.
• “Compressing a gas always heats it.” Repair ΔU = q + W. If more energy leaves by heating than the work done on the gas, U and T fall (worked example 2).
• “ΔV in cm3 goes straight into pΔV.” Repair Convert to m3 (1 cm3 = 1.0 × 10−6 m3) so that Pa × m3 gives joules.

• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.
• Say which part of U changes. “The internal energy increases” is true for both a temperature rise and melting, so on its own it explains neither. The explanation is in naming the part: mean kinetic energy of the molecules (temperature rises) or potential energy of the molecules (temperature constant, change of state).
• Two habits worth building. Read the y-intercept by substituting a point into y = mx + c whenever the axis starts at a false origin; and give the uncertainty in the gradient as the difference between the best-fit and the worst acceptable gradient, not a guess. Name a specific source of uncertainty, such as the ±0.5 cm3 reading of the syringe; “human error” names nothing that could be measured or improved.
• Interleave with the chapters that use this one. When you reach topic 17, re-answer: which energy stores does an oscillator exchange, and what stays constant? When you reach topic 19, re-answer: why is the energy stored by a capacitor an area under a graph, as the work done by a gas is? Recalling a topic inside a new context is worth more than another pass over this chapter on its own; at A Level, Paper 4 assumes the whole of the AS content, so nothing here is ever finished with.

• Cambridge International AS & A Level Physics 9702 has five components. Topic 16 is A Level content, so it is examined in Papers 4 and 5. A Level content: examined in Paper 4 (A Level structured, which also requires the AS content) and, as practical context, Paper 5. AS Level candidates take Papers 1, 2 and 3; A Level candidates take all five, either staged over two years (Papers 1–3 in year one, Papers 4 and 5 in year two) or together in one series. Examinations are available in the June and November series, and in March in India.
• Across both the AS Level and the A Level the assessment objectives are weighted AO1 40% (knowledge and understanding), AO2 40% (handling, applying and evaluating information) and AO3 20% (experimental skills and investigations). AS candidates are graded a–e; A Level candidates A*–E. The Data and formulas sheet is printed as page 2 of Papers 1 and 2 and as pages 2 and 3 of Paper 4: it gives the constants and a short list of formulas. Every other equation in this chapter is one the syllabus says you must recall, and this chapter says which is which.
• There is no multiple-choice paper on A Level content, so Topic 16 appears in Paper 4 structured questions. Expect to define or state internal energy and the first law in words, to explain why the internal energy of an ideal gas depends only on temperature, and to explain a temperature change (or its absence) using the first law with the sign of every term stated.
• Calculations of W from pΔV or from an area under a p–V graph, a table of ΔU, q and W for each stage of a cycle, and U = (3/2)nRT for a monatomic ideal gas. Neither W = pΔV nor ΔU = q + W is on the Data and formulas sheet: both are recall. R and k are given.
• The syllabus names no experiment for this topic, but a gas syringe in a water bath is a natural Paper 5 context: vary the temperature, measure the volume at constant pressure, plot V against θ, and find the amount of gas and the work done from the gradient. The largest uncertainty is usually the volume change, a difference of two readings.
• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.