Q.Find the temperature at which the readings of the Fahrenheit and Celsius scales are equal.
🔒You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.
🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Temperature Scale Conversion
Temperature Scale Conversion
You already know temperature as a measure of hotness or coldness. But here's the thing: different countries and different scientific fields measure that same hotness using different numbers. Water boils at 100 on the Celsius scale, but at 212 on the Fahrenheit scale. That's not because the water is different — it's because the rulers are different.
The core idea
A temperature scale is just a number line someone decided to draw on the same physical reality. Converting between scales means finding the number on one number line that corresponds to the same physical hotness as a given number on another number line.
Think of it like this: if you measure a table's length in feet and get 6, and I measure it in metres and get 1.83, we're both describing the same table. Temperature conversion works exactly the same way — same physical state, different numbers.
The three main scales you'll meet
| Scale | Freezing point of water | Boiling point of water | Used by |
|---|---|---|---|
| Celsius (°C) | 0 | 100 | Most of the world, science |
| Fahrenheit (°F) | 32 | 212 | USA, a few other countries |
| Kelvin (K) | 273.15 | 373.15 | All scientific work |
Notice something: Celsius and Kelvin have the same step size — a change of 1°C is exactly a change of 1 K. They just start at different places. Fahrenheit has a smaller step size (180 steps between freezing and boiling, instead of 100).
The conversion formulas
°F=59(°C)+32
°C=95(°F−32)
K=°C+273.15
These aren't magic. Each one comes from the simple idea of matching two number lines.
Why the formulas look like that
Between freezing and boiling water:
- Celsius has 100 steps (0 to 100)
- Fahrenheit has 180 steps (32 to 212)
So one Celsius step is 100180=59 Fahrenheit steps. That's the 59 factor. The +32 just shifts the starting point — because 0°C doesn't correspond to 0°F, it corresponds to 32°F.
For Kelvin: since the step size is identical to Celsius, you just add the offset. The 273.15 comes from the fact that absolute zero (the coldest possible temperature) is 0 K, which is −273.15°C.
A worked example
Convert 25°C to Fahrenheit.
Step 1: Multiply by 59.
25×59=25×1.8=45
Step 2: Add 32.
45+32=77
So 25°C = 77°F. A warm spring day in Celsius terms is 77°F — same weather, different number.
For quick mental estimates: double the Celsius and add 30. It's not exact (you get 80 instead of 77 here), but it's close enough for everyday "should I wear a jacket?" decisions.
The one thing students mess up …
The Celsius and Fahrenheit scales are related by C/5 = (F − 32)/9; setting C = F and solving gives the one temperature where both scales read the same number. …
The Celsius and Fahrenheit scales coincide at −40° — that is, −40°C = −40°F.
The relation between the Celsius (C) and Fahrenheit (F) scales is:
C/5 = (F − 32)/9
We want the temperature at which the numerical readings are equal, so set C = F = x:
x/5 = (x − 32)/9
Cross-multiplying:
9x = 5(x − 32)
9x = 5x − 160
9x − 5x = −160
4x = −160
x = −40
…
Showing the 12 most recent of 23 on this concept.
- CBSE 2026Set ANNUAL1 markQ.Fill in the blank: The boiling point of water is ______ Celsius at 1.013 bar pressure.
›Reveal solutionSolution
Water's normal boiling point, at standard atmospheric pressure of 1.013 bar, is 100°C (373.15 K).
The boiling point of a liquid is the temperature at which its vapour pressure equals the external (atmospheric) pressure. This value depends on the surrounding pressure — at lower pressures (e.g., high altitude) water boils at a lower temperature, and at higher pressures it boils at a higher temperature. The standard atmospheric pressure …
- CBSE 2026Set ANNUAL1 markMCQQ.The temperature at which Celsius temperature and Fahrenheit temperature are equal, is(a) 0°(b) 40°(c) − 40°(d) − 32°
›Reveal solutionSolution
Celsius and Fahrenheit are equal at -40 degrees. Answer (C).
The conversion is F = (9/5)C + 32. Set F = C = x:
x = (9/5)x + 32
x - (9/5)x = 32
-(4/5)x = 32
x = -40.
…
- CBSE 2025Set ANNUAL1 markMCQQ.The temperature which have same numerical value in Celsius and Fahrenheit scales is (A) 40° (B) -40°C (C) 100° (D) 273°
›Reveal solutionSolution
The Celsius and Fahrenheit scales read the same numerical value at -40°.
The relation between Celsius (C) and Fahrenheit (F) scales is:
5C=9F−32
Setting C=F (equal numerical value) and solving:
…
- CBSE 2025Set hz1 markMCQQ.On the basis of absolute zero as the scale of temperature, the ice melts at:(a) 100 degrees(b) 273.15 K(c) 373.15 K(d) None of them
›Reveal solutionSolution
The Kelvin scale is defined so that its zero coincides with absolute zero, and the ice point (0 degree C, where ice melts under standard pressure) is 273.15 K on this scale.
The absolute (Kelvin) temperature scale is related to the Celsius scale by:
T(K) = T(degree C) + 273.15
The melting point of ice (the ice point) under standard atmospheric pressure is 0 degree C by definition of the Celsius scale. Converting this to the Kelvin scale:
T(K) = 0 + 273.15 = 273.15 K
…
- CBSE 2024Set ANNUAL1 markMCQQ.The temperature of a body is found in Kelvin scale as x K and in Fahrenheit scale x°F. The value of x will be (A) 574.25 (B) 301.25 (C) 335 (D) 365
›Reveal solutionSolution
The temperature at which the Kelvin and Fahrenheit numerical values coincide is x=574.25.
Conversion: °F=59(K−273)+32. Setting both readings equal to x: x=59(x−273)+32.
…
- CBSE 2024Set SET-AP55001 markMCQQ.The relation between the Centigrade (Celsius) temperature scale and the Kelvin temperature scale is:(a) c = k - 273(b) c = k + 273(c) c = k + 100(d) c = k - 100
›Reveal solutionSolution
The Celsius and Kelvin scales have the same size of degree but different zero points: 0°C = 273 K (more precisely 273.15 K), so C = K − 273.
The Kelvin scale starts at absolute zero (0 K), while the Celsius scale sets 0°C at the freezing point of water. The freezing point of water is 273.15 K, so to convert from Kelvin to Celsius you subtract 273 (approximately): …
- CBSE 2024Set SET-AP55001 markQ.At what temperature will the readings of the Fahrenheit and Celsius scales be equal?
›Reveal solutionSolution
The Fahrenheit and Celsius scales give the same numerical reading at exactly −40 degrees.
The conversion between the two scales is:
F = (9/5)C + 32
Setting F = C (both readings equal, call the common value x):
x = (9/5)x + 32
x − (9/5)x = 32
−(4/5)x = 32
x = 32 × (−5/4) = −40
…
- CBSE 2024Set ANNUAL1 markMCQQ.The SI unit of temperature is(a) A) °C(b) B) °F(c) C) K(d) D) Kg
›Reveal solutionSolution
[!TLDR]
C) K
Why
Kelvin is the SI base unit of thermodynamic …
- CBSE 2023Set ANNUAL1 markMCQQ.SI unit of temperature is(a) Kelvin(b) Celsius(c) Fahrenheit(d) Centigrade
›Reveal solutionSolution
Kelvin is the SI base unit for temperature; Celsius, Fahrenheit and Centigrade are common but non-SI temperature scales.
The International System of Units (SI) defines seven base units, one for each fundamental physical quantity. For temperature, the SI base unit is the kelvin (K), defined via the thermodynamic (absolute) temperature scale, with 0 K = absolute zero. Celsius (°C) is an SI-accepted derived scale (T(K) = …
- CBSE 2023Set ANNUAL1 markMCQQ.Temperature difference of 20°C is equivalent to:(a) 20 K(b) 293 K(c) 253 K(d) 0 K
›Reveal solutionSolution
Celsius and Kelvin scales have identically sized degrees, so a temperature DIFFERENCE of 20 degC is exactly 20 K -- only absolute temperature readings differ by the 273 offset, not temperature intervals.
The relation between an absolute Celsius reading and Kelvin reading is T(K) = T(degC) + 273. For two temperatures T1 and T2 in Celsius, converting both to Kelvin:
T1(K) = T1(degC) + 273
T2(K) = T2(degC) + 273
Subtracting: T2(K) - T1(K) = T2(degC) - T1(degC)
…
- CBSE 2023Set ANNUAL1 markMCQQ.Absolute zero of temperature is:(a) 100°C(b) 273°C(c) −273°C(d) −273.15°C
›Reveal solutionSolution
Absolute zero = −273.15 °C = 0 K.
The Kelvin (absolute) scale is related to Celsius by T(K) = t(°C) + 273.15. At absolute zero T = 0 K, so t = −273.15 °C. This is the lowest temperature theore …
- CBSE 2023Set ANNUAL1 markMCQQ.Temprature which has equal reading on Celcius and Faherenhit scale:(a) 0°(b) 30°(c) −40°(d) 40°
›Reveal solutionSolution
The two scales agree at −40°.
The Celsius–Fahrenheit relation is F = (9/5)C + 32. For equal readings put F = C = x:
…
🎓Unlock everything free for 14 days
- ✓Full step-by-step solutions
- ✓Concept-first explanations
- ✓Methods, shortcuts & mistakes
- ✓PYQ mapping + timed mock tests
Full access for 14 days. No credit card required.