Temperature

• Temperature sets the direction; energy per kilogram sets the amount. A temperature difference is the same number in K and °C, but a temperature in an equation is in kelvin.
• Net transfer from higher to lower temperature. Per unit mass, per kelvin; per unit mass, at constant temperature. Losses to the room make c and Lv too large; gains from the room make an uncorrected Lf too small. Two powers and a control funnel take them out.

• 14.1.1 I can understand — understand that (thermal) energy is transferred from a region of higher temperature to a region of lower temperature
• 14.1.2 I can understand — understand that regions of equal temperature are in thermal equilibrium
• 14.2.1 I can understand — understand that a physical property that varies with temperature may be used for the measurement of temperature and state examples of such properties, including the density of a liquid, volume of a gas at constant pressure, resistance of a metal, e.m.f. of a thermocouple
• 14.2.2 I can understand — understand that the scale of thermodynamic temperature does not depend on the property of any particular substance
• 14.2.3 I can convert — convert temperatures between kelvin and degrees Celsius and recall that T / K = θ / °C + 273.15
• 14.2.4 I can understand — understand that the lowest possible temperature is zero kelvin on the thermodynamic temperature scale and that this is known as absolute zero
• 14.3.1 I can define — define and use specific heat capacity
• 14.3.2 I can define — define and use specific latent heat and distinguish between specific latent heat of fusion and specific latent heat of vaporisation

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.

• “A rise from 20 °C to 60 °C is a rise of 313 K.” Correct A temperature difference is the same number in K and °C, but a temperature in an equation must be in K. The rise is 40 K. Add 273.15 only when you convert a temperature, never a difference. In E = mcΔθ either unit gives the same Δθ; in any equation that uses T itself (topics 15 and 16), the temperature must be in kelvin.
• “Energy flows from the object with more energy to the one with less.” Correct The net transfer is from higher to lower temperature. A bath at 40 °C holds far more energy than a spark at 1000 °C, yet the spark heats the bath.
• “In thermal equilibrium no energy moves between the two objects.” Correct Energy still moves both ways; there is no net transfer, because the temperatures are equal.
• “Two thermometers calibrated at 0 °C and 100 °C must agree at 50 °C.” Correct They agree at the fixed points and generally disagree between them, because each scale assumes its own property varies linearly, and different properties do not vary in exactly the same way.
• “Specific heat capacity is the energy needed to raise the temperature of an object by 1 °C.” Correct Per unit mass: the energy required per unit mass of the substance to raise its temperature by one kelvin, unit J kg−1 K−1.
• “Heat losses make the measured specific heat capacity too small.” Correct Less energy reaches the block than VIt, so its temperature rise is smaller and c = VIt/(mΔθ) comes out too large. The same is true of Lv measured with boiling water. Melting ice is the exception: it is colder than the room and gains energy from it, so an uncorrected Lf comes out too small (worked example 6).
• “Absolute zero is 0 °K.” Correct The unit is the kelvin, symbol K. It is never written with a degree sign, and it is read “zero kelvin”, with no “degree” in it.
• “Heat flows from the object with more energy to the one with less.” Repair There is a net transfer of thermal energy from the region of higher temperature to the region of lower temperature, whatever the amounts of energy they hold.
• “Thermal equilibrium means no energy is exchanged.” Repair It means no net transfer of thermal energy; energy still passes both ways, in equal amounts, because the temperatures are equal.
• “Two correctly calibrated thermometers always agree.” Repair They agree at the fixed points. Based on different properties, they generally disagree between them, because each assumes its own property varies linearly with temperature.
• “The thermodynamic scale is the Celsius scale of a mercury thermometer, shifted by 273.” Repair The thermodynamic scale does not depend on the property of any particular substance. Mercury, like every substance, defines only its own scale.
• “A rise of 30 °C is a rise of 303 K.” Repair A temperature difference is the same number in both units: 30 K. Only a temperature is converted by adding 273.15.
• “Specific heat capacity is the energy needed to raise the temperature of an object by 1 °C.” Repair The energy required per unit mass of the substance to raise its temperature by one kelvin; unit J kg−1 K−1.
• “During melting the temperature is steady because no energy is being supplied.” Repair Energy is supplied throughout; it increases the potential energy of the molecules as they separate, not their average kinetic energy, so the temperature does not change.
• “Lv is bigger than Lf because boiling happens at a higher temperature.” Repair The temperature has nothing to do with it. Vaporising separates the molecules completely (melting only slightly), and the large volume increase means work is done pushing back the atmosphere.
• “Heat losses make the measured c too small.” Repair Less energy reaches the block than VIt, so Δθ is smaller and c = VIt/(mΔθ) is too large.
• “The control funnel is there to check that the heater works.” Repair Its heater is switched off. It measures the mass of ice melted by energy from the surroundings, which is subtracted from the heated funnel’s mass.

• 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 “net” and say “temperature”. “Heat flows from hot to cold” is the O Level version. The A Level statement is: there is a net transfer of thermal energy from the region of higher temperature to the region of lower temperature.
• Ask one question before you add 273.15: is this a temperature, or a change in temperature? Only a temperature is converted.
• Losses are a systematic error, not a random one. They push every repeat the same way, so averaging repeats does not remove them. A value that differs from the accepted one by more than its measurement uncertainty is the sign of a systematic error; the practical dataset shows that test.
• Interleave with the chapters that use this one. Topic 15 (ideal gases) uses the kelvin in pV = nRT and explains temperature as molecular kinetic energy: when you reach it, re-answer “why must T be in kelvin?”. Topic 16 (thermodynamics) names the molecular kinetic and potential energies internal energy: re-answer “why is the temperature constant while ice melts?” in its language. 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 14 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.
• A Paper 4 structured question can ask you to define specific heat capacity or specific latent heat, to state what is meant by thermal equilibrium or absolute zero, to explain why the temperature stays constant during a change of state, why Lv is larger than Lf, or why two thermometers disagree between their fixed points. Paper 4 assumes the AS content, so energy conservation and P = VI are used without being re-taught.
• Kelvin–Celsius conversions, E = mcΔθ and E = mL alone and together (heating then boiling, ice melting in a drink), calibration by linear interpolation, and loss-cancelling results such as L = (P1 − P2)t/(Δm1 − Δm2). None of the equations of this topic is on the Data and formulas sheet: T / K = θ / °C + 273.15, E = mcΔθ, E = mL and P = VI are all recall. Values of c and L are given in the question.
• Electrical heating of a block or liquid is a standard planning and analysis context: time is varied, temperature is measured with a thermometer reading to 0.1 °C, the gradient of θ against t gives c, and energy lost to the surroundings is the largest, systematic, error. For latent heat, a graph of mass boiled off against heater power gives Lv from its gradient and the loss rate from its intercept.
• 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.