Q.Two temperature scales A and B are related by a straight-line graph on which temperature on scale A (in °A) is plotted on the vertical axis and temperature on scale B (in °B) on the horizontal axis. Between the lower fixed point and the upper fixed point there are 150 equal divisions on scale A and 100 equal divisions on scale B. The straight line passes through the lower fixed point at $30\,^\circ$A (which reads $0\,^\circ$B) and the upper fixed point at $180\,^\circ$A (which reads $100\,^\circ$B). The relationship for conversion between the two scales is given by

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

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

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 $\frac{180}{100} = \frac{9}{5}$ Fahrenheit steps. That's the $\frac{9}{5}$ 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 $\frac{9}{5}$.

Step 2: Add 32.

So 25°C = 77°F. A warm spring day in Celsius terms is 77°F — same weather, different number.

The one thing students mess up

Why Kelvin matters

Kelvin is the scientist's scale because it starts at absolute zero — the point where particles have minimum possible thermal motion. This makes all gas laws and thermodynamic equations simple. You'll never see a negative Kelvin temperature in normal physics; 0 K is the floor.

When a problem gives you Celsius and the formula uses Kelvin (like the ideal gas law $PV = nRT$), you must convert: $K = °C + 273.15$.

The big picture

Temperature scale conversion is just relabelling the same physical reality. The formulas are linear — multiply to adjust step size, add to adjust zero point. Once you see that, every conversion is just arithmetic.

For quick revision, remember that Temperature Scale Conversion is drawn directly from the Thermal Properties of Matter coverage of the NCERT/CBSE Class 11 Physics syllabus and recurs often in JEE Main and NEET papers, which is exactly why "Temperature Scale Conversion important questions" shows up so often in Physics question banks. The clearest way to build exam confidence here is to combine this explanation with the NCERT Physics textbook's own solved examples and chapter-end questions.