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

Temperature Scales

Learning Objective

Understand that a physical property which varies with temperature can be used to measure temperature, and be able to state examples such as the density of a liquid, the volume of a gas at constant pressure, the resistance of a metal, and the e.m.f. of a thermocouple.

1. Common Temperature Scales

Temperature is a quantitative measure of the average kinetic energy of particles in a substance. Several scales are used in physics and everyday life:

• Celsius (°C): Defined by the freezing point (0 °C) and boiling point (100 °C) of water at 1 atm.
• Fahrenheit (°F): Freezing point of water is 32 °F and boiling point is 212 °F at 1 atm.
• Kelvin (K): Absolute temperature scale; 0 K is absolute zero. The size of one kelvin is the same as one degree Celsius.
• Rankine (°R): Absolute scale based on Fahrenheit degrees; 0 °R is absolute zero.

Conversion formulas:

• \$T{\text{K}} = T{\text{°C}} + 273.15\$
• \$T{\text{°F}} = \frac{9}{5}T{\text{°C}} + 32\$
• \$T{\text{°R}} = \frac{9}{5}T{\text{K}}\$

2. Principle of Using Physical Properties as Thermometers

A thermometer works on the principle that a measurable physical property \$P\$ changes in a predictable way with temperature \$T\$. If the relationship \$P(T)\$ is known and monotonic over the range of interest, the temperature can be deduced by measuring \$P\$.

Key requirements for a good thermometric property:

1. Strong, reproducible dependence on temperature.
2. Linear (or easily linearised) relationship over the required range.
3. Minimal dependence on other variables (e.g., pressure, composition).
4. Stability and ease of measurement.

3. Examples of Temperature‑Dependent Properties

3.1 Density of a Liquid

For many liquids the density \$\rho\$ decreases with increasing temperature. Over a limited range the variation can be approximated by

\$\rho(T) \approx \rho0\bigl[1 - \beta (T - T0)\bigr]\$

where \$\beta\$ is the volumetric expansion coefficient. A classic example is the use of a mercury or alcohol column in a glass thermometer.

3.2 \cdot olume of a Gas at Constant Pressure

At constant pressure, the volume \$V\$ of an ideal gas varies linearly with absolute temperature (Charles’s law):

\$\frac{V}{T} = \text{constant} \quad\Longrightarrow\quad V = V0\frac{T}{T0}\$

This principle underlies gas‑filled thermometers and the operation of a constant‑pressure gas thermometer.

3.3 Electrical Resistance of a Metal

For many metals the resistance \$R\$ increases approximately linearly with temperature:

\$R = R0\bigl[1 + \alpha (T - T0)\bigr]\$

where \$\alpha\$ is the temperature coefficient of resistance. Platinum resistance thermometers (PRTs) exploit this relationship.

3.4 e.m.f. of a Thermocouple

A thermocouple consists of two dissimilar metals joined at one end. A temperature difference \$\Delta T = T{\text{hot}} - T{\text{cold}}\$ generates an e.m.f. \$E\$ that, for small ranges, is linear:

\$E = a\,\Delta T\$

where \$a\$ is the Seebeck coefficient (specific to the metal pair). Thermocouples are widely used for rapid temperature measurements.

4. Comparative Summary of Thermometric Properties

5. Concluding Remarks

Any physical quantity that varies in a known, monotonic way with temperature can serve as a thermometer. The choice of property depends on the required temperature range, accuracy, response time, and practical considerations such as durability and cost. Mastery of these principles enables the selection and use of appropriate temperature‑measuring devices in experimental physics and engineering.