convert temperatures between kelvin and degrees Celsius and recall that T / K = θ / °C + 273.

Temperature Scales

Learning Objective

By the end of this lesson you will be able to:

• Convert temperatures between kelvin (K) and degrees Celsius (°C).
• Recall and apply the relationship $\displaystyle \frac{T}{\text{K}} = \frac{\theta}{^\circ\text{C}} + 273$.

Why Two Scales?

The kelvin scale is an absolute temperature scale – 0 K is the theoretical point at which all molecular motion ceases. The Celsius scale is a relative scale anchored to the freezing and boiling points of water at 1 atm.

Key Relationship

The conversion between the two scales is linear and can be written as:

$$T\ (\text{K}) = \theta\ (\text{°C}) + 273.15$$

For most A‑Level work the approximation 273 is acceptable, but the more precise value is 273.15 K.

Conversion Formulas

From	To	Formula	Example
°C	K	$T = \theta + 273.15$	$25^\circ\text{C} \rightarrow 298.15\ \text{K}$
K	°C	$\theta = T - 273.15$	$310\ \text{K} \rightarrow 36.85^\circ\text{C}$

Worked Examples

1. Convert 0 °C to kelvin.

   Using $T = \theta + 273.15$:

   $$T = 0 + 273.15 = 273.15\ \text{K}$$

2. Convert 500 K to degrees Celsius.

   Using $\theta = T - 273.15$:

   $$\theta = 500 - 273.15 = 226.85^\circ\text{C}$$

3. Find the temperature in kelvin of a laboratory oven set at 200 °C.

   $$T = 200 + 273.15 = 473.15\ \text{K}$$

Common Mistakes

• Adding or subtracting 273 instead of 273.15 when high precision is required.
• Confusing the symbols: $T$ is always in kelvin, $\theta$ (or $t$) is in degrees Celsius.
• Forgetting that the kelvin scale has no negative values – any calculation that yields $T < 0$ K indicates an error.

Practice Questions

1. Convert $-40^\circ\text{C}$ to kelvin.
2. A gas is heated from $300\ \text{K}$ to $450\ \text{K}$. What is the temperature change in degrees Celsius?
3. The temperature of a star is $5800\ \text{K}$. Express this temperature in degrees Celsius.
4. Explain why the statement “$0^\circ\text{C}$ is the same as $0\ \text{K}$” is false, using the conversion formula.

Summary

The conversion between kelvin and degrees Celsius is straightforward because the two scales are offset by a constant value:

$$\boxed{T\ (\text{K}) = \theta\ (\text{°C}) + 273.15}$$

Remember to keep track of units, use the correct sign, and apply the precise offset when required.