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

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.