Physics 9702 · Paper 4

Practical Thermometers

Any property that changes steadily with temperature can measure it. Paper 4 focuses on two electrical sensors — the thermistor and the thermocouple — and one ideal reference, the gas thermometer.

Thermistor and thermocouple

A is a semiconductor whose resistance falls as temperature rises (more charge carriers are freed at higher temperature). Measure the resistance, read off the temperature. You met it as a sensor in AS circuits; here it becomes a thermometer.
A is two wires of different metals joined at two junctions. When the junctions sit at different temperatures, an e.m.f. appears across the free ends — the bigger the temperature difference, the bigger the e.m.f.

A thermocouple: two different metals, two junctions. The e.m.f. read by the voltmeter depends on the temperature difference between the junctions — small, fast, and able to measure at a point.

The junction is tiny, so a thermocouple has a small thermal capacity: it takes almost no energy from the sample, reacts quickly, and measures the temperature at a point. That is why it is the choice for a rapidly changing temperature (9702/41/M/J/24 Q2(b)(iii)).

Feature	Thermistor	Thermocouple
What is measured	resistance (falls as θ rises)	e.m.f. between two junctions
Response	slower — larger thermal capacity	fast — tiny junction, small thermal capacity
Where it measures	over the body of the sensor	at a point (the junction)
Range	narrow	very wide (junction metals chosen to suit)
Linearity	non-linear over a narrow range	non-linear — needs calibration

Neither sensor responds linearly, so both need calibration: record the output at known temperatures, plot the curve, then read unknown temperatures from the curve — never assume equal output steps mean equal temperature steps.

The gas thermometer idea

The thermodynamic scale needs an instrument that does not depend on one substance's habits. A near-ideal gas at constant volume provides it: pressure is proportional to thermodynamic temperature, and this works the same for any gas that is close to ideal.
So a constant-volume gas thermometer converts a pressure ratio directly into a temperature ratio: $\dfrac{p_1}{p_2} = \dfrac{T_1}{T_2}$ . A 2025 paper asked for exactly this reasoning and calculation (9702/42/O/N/25 Q3(b)).

Worked example

9702-style: pressure ratio to temperature

A fixed volume of gas has pressure 5.00 kPa at 273.2 K. In a cold room the pressure falls to 4.32 kPa. Find the room temperature in °C.

Pressure ratio equals temperature ratio: $T = 273.2 \times \dfrac{4.32}{5.00} = 236\ \text{K}$ .
Convert: $\theta = 236 - 273.15 = -37\ {}^{\circ}\text{C}$ .

Answer

\theta \approx -37\ {}^{\circ}\text{C}

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