Temperature, Heat & Thermometry – Complete JEE & NEET Guide
Thermal physics begins with understanding the dual concepts of heat and temperature. While often conflated in everyday conversation, they represent fundamentally distinct physical quantities: heat is energy in transit across a boundary due to a temperature difference, whereas temperature is a thermodynamic state variable characterizing the thermal state of matter.
- Heat (Q): Energy transferred between a system and its surroundings by virtue of temperature difference alone. SI unit: Joule (J); practical unit: calorie (cal) (1 cal = 4.186 J).
- Temperature (T): Macroscopic property that governs the direction of net spontaneous heat flow (from higher temperature to lower temperature). Microscopic interpretation: proportional to the average translational kinetic energy per molecule (Ek = (3/2) kB T). SI unit: Kelvin (K).
1. Thermal Equilibrium & Zeroth Law of Thermodynamics
Two bodies are said to be in thermal equilibrium when they are in thermal contact and there is no net exchange of heat energy between them, which implies they are at the identical temperature.
Zeroth Law of Thermodynamics (R.H. Fowler, 1931)
“If two systems A and B are separately in thermal equilibrium with a third system C, then they are also in thermal equilibrium with each other.”
This fundamental law serves as the operational basis of temperature measurement: the third body C acts as a thermometer. If C indicates the same temperature when brought into contact with A and B separately, A and B are in thermal equilibrium.
2. Thermometry & Thermometric Properties
A thermometer measures temperature by exploiting a measurable physical property that changes continuously and monotonically with temperature, called a thermometric property (X).
| Thermometer Type | Thermometric Property (X) | Linear Working Formula | Typical Useful Range |
|---|---|---|---|
| Mercury-in-glass | Length / volume of mercury column (L) | T = [(LT − L0) / (L100 − L0)] × 100 °C | −39 °C to 357 °C |
| Constant-Volume Gas | Pressure of a fixed mass of gas (P) | T = [(PT − P0) / (P100 − P0)] × 100 °C | −270 °C to 1500 °C |
| Platinum Resistance | Electrical resistance of wire (R) | RT = R0(1 + α T + β T2) | −200 °C to 1200 °C |
| Thermoelectric (Thermocouple) | Seebeck thermoelectric EMF (ε) | ε = a T + b T2 | −200 °C to 1600 °C |
| Optical Pyrometer | Intensity of emitted thermal radiation | Wien's law / Stefan's law calibration | > 800 °C to 4000 °C (e.g., Sun) |
3. Standard Temperature Scales & Conversion Relations
Traditionally, temperature scales were calibrated between two reproducible reference points: the ice point (melting point of pure ice at 1 atm) and the steam point (boiling point of pure water at 1 atm).
(Reading on Scale − Lower Fixed Point) / (Upper Fixed Point − Lower Fixed Point) = Constant
C / 100 = (F − 32) / 180 = (K − 273.15) / 100 = R / 80
Simplifying the ratio of 100 : 180 : 100 gives the classic relation:
Change in Temperature (ΔT) Relations
A change in temperature does NOT involve constant offsets:
- ΔC = ΔK (each division is identical in magnitude)
- ΔF = (9/5) ΔC = 1.8 ΔC
- ΔC = (5/9) ΔF
Example: An increase of 25 °C corresponds to an increase of 25 K and an increase of 45 °F.
Critical Intersection Points for JEE
- Celsius & Fahrenheit coincide: C = F = −40° (−40 °C = −40 °F).
- Fahrenheit & Kelvin coincide: F = K = 574.59° (574.59 °F = 574.59 K; 574.25 if K = C + 273 is used).
- Celsius & Kelvin NEVER coincide: Since K = C + 273.15, their difference is strictly 273.15.
4. The Absolute Temperature Scale & Ideal Gas Thermometer
Experiments on different low-density real gases (Hydrogen, Helium, Nitrogen) in constant-volume gas thermometers reveal that plots of pressure (P) versus temperature (°C) are straight lines. When extrapolated backwards to zero pressure (P → 0), all curves intersect the temperature axis at the exact same temperature: −273.15 °C.
This universal point represents the absolute minimum temperature theoretically achievable – the Absolute Zero (0 K = −273.15 °C) – at which molecular translational kinetic energy approaches zero.
5. Modern Standard: Triple Point of Water
In modern international metrology (SI), the Kelvin scale is defined with respect to a single, unvarying fixed point: the Triple Point of Water (where pure ice, liquid water, and saturated water vapour coexist in dynamic equilibrium).
- Temperature: Ttr = 273.16 K = 0.01 °C.
- Vapour Pressure: Ptr = 611.65 Pa ≈ 4.58 mmHg ≈ 0.006 atm.
In a constant-volume gas thermometer, the absolute temperature T of any body is given by:
Taking the limit as gas pressure approaches zero ensures that the gas behaves ideally, rendering the measurement independent of the specific chemical nature of the gas.
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