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Temperature conversion looks like the easiest marks in thermal physics, yet it trips students in two ways: they confuse a temperature with a temperature difference, and they freeze when a question invents its own scale. This post explains why thermometers work at all, then gives one formula that handles every linear scale, with five worked examples.
What does the zeroth law say, and why does it matter?
The NCERT Class 11 chapter Thermodynamics states the zeroth law as: "two systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other". NCERT describes the set-up: systems A and B are each in contact with C through conducting walls but separated from each other by an insulating wall. Once both reach equilibrium with C, connecting A and B causes no further change.
That third system is your thermometer. When a thermometer reaches equilibrium with your body and later with a bath, and shows the same reading, the zeroth law tells you that your body and the bath would be in equilibrium with each other. Temperature is the property they share. NCERT notes that the zeroth law led to the concept of temperature.
The Syllabus for JEE (Main) 2026 lists "thermal equilibrium and the concept of temperature, zeroth law of thermodynamics" in the Thermodynamics unit. Check the syllabus for your exam year.
How are temperature scales built?
A thermometer uses a property that changes steadily with temperature: the length of a mercury column, the resistance of a wire, the pressure of a gas. The NCERT chapter Thermal Properties of Matter uses two fixed points, the ice point and the steam point, which are 0 °C and 100 °C on the Celsius scale and 32 °F and 212 °F on the Fahrenheit scale. There are 100 divisions between them on one scale and 180 on the other, which gives
(tF − 32) / 180 = tC / 100.
The same idea works for any linear scale:
(reading − lower fixed point) / (upper fixed point − lower fixed point) is the same on every scale.
NCERT also gives T = tC + 273.15 for the Kelvin scale. The kelvin itself is now defined without water at all. According to the BIPM, it is defined "by taking the fixed numerical value of the Boltzmann constant k to be 1.380 649 × 10⁻²³" J/K.
Five worked examples
1. Body temperature. Convert 37.0 °C to Fahrenheit and Kelvin. tF = (9/5) × 37.0 + 32 = 66.6 + 32 = 98.6 °F. T = 37.0 + 273.15 = 310.15 K.
2. Where do Celsius and Fahrenheit agree? Set tF = tC = x: x = (9/5)x + 32, so −(4/5)x = 32 and x = −40. So −40 °C = −40 °F.
3. A made-up scale. On scale X, ice melts at −20 °X and water boils at 180 °X. Convert 50 °C. (X − (−20)) / 200 = 50 / 100, so X + 20 = 100 and X = 80 °X. A change of 1 °C is a change of 2 °X.
4. A faulty thermometer. A Celsius thermometer reads 5° in melting ice and 95° in steam. It reads 41°. What is the true temperature, and at what reading is it correct? True t / 100 = (41 − 5) / (95 − 5) = 36 / 90, so t = 40 °C. It is correct where reading = true value: (x − 5)/0.9 = x, so x − 5 = 0.9x and x = 50 °C.
5. A resistance thermometer. A platinum wire has resistance 10.0 Ω at the ice point and 13.9 Ω at the steam point. Assuming a linear change, what temperature gives 11.5 Ω? t = (11.5 − 10.0) / (13.9 − 10.0) × 100 = 1.5 / 3.9 × 100 ≈ 38.5 °C.
Example 5 is the same formula as example 3. The property changes, the method does not.
Which mistakes are most common?
Adding 32 or 273.15 to a difference. A 20 K rise is a 20 °C rise, and a 36 °F rise.
Writing °K. The unit is the kelvin, symbol K, with no degree sign.
Using Celsius in gas laws. PV = nRT and other thermodynamic formulas need kelvin.
Assuming a faulty thermometer is wrong everywhere. With a wrong zero and a wrong scale size, there is usually one reading where it is exactly right.
Thinking the zeroth law is obvious, so useless. It is the reason a single thermometer can compare any two objects.
A practice routine
Write the general ratio formula from memory at the start of each session.
Make three invented scales with odd fixed points and convert 0 °C, 37 °C and 100 °C into each.
Do two difference problems for every temperature problem, so the habit sticks.
Then move to heat calculations: our guides to calorimetry and heat transfer and thermal expansion problems both depend on getting temperature changes right.
If the idea of equilibrium between systems feels shaky, the Fermi Concept Library covers every concept in physics with its own lesson, so you can revise thermal equilibrium before attempting the harder problems.
Start now: convert your city's temperature today into kelvin, Fahrenheit and a scale you invent.
