Temperature and specific heat

01Why this matters

A large pot of water needs more energy than a small cup for the same temperature rise. Temperature change alone does not determine the energy needed.

02See it

03Understand it

Temperature describes thermal state. Specific heat capacity is the energy required to raise one kilogram of a substance by one kelvin.

For a substance with approximately constant specific heat and no phase change, Q = mcΔT. Mass is in kilograms and specific heat in J/(kg·K). A temperature difference of 1 °C equals a difference of 1 K. This does not mean the absolute Celsius and kelvin temperature readings are equal.

04Guided example

Heat 0.5 kg of water by 10 °C, using c = 4,200 J/(kg·K), with no losses.

1. Identify m = 0.5 kg and ΔT = 10 K.
2. Multiply mass and specific heat: 0.5 × 4,200 = 2,100 J/K.
3. Multiply by temperature rise: Q = 2,100 × 10 = 21,000 J.

05Try it

06Practise it

07Use it in the real world

A heater must supply more than the ideal calculated energy if the container and surroundings also warm up. Heating time estimates need both power and an efficiency assumption.

08Quick check

09Summary

Temperature describes thermal state. Specific heat capacity is the energy required to raise one kilogram of a substance by one kelvin. Multiply by temperature rise: Q = 2,100 × 10 = 21,000 J.

Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.

10Key idea