08 · 18 min
Heating
Specific heat capacity, latent heat, and why temperature is not heat.
E = mcΔθ
The idea
Temperature is a measure of how hot something is, linked to the average kinetic energy of its particles. Heat, or heating, is energy transferred because of a temperature difference. A bath of lukewarm water can store more thermal energy than a cup of boiling water.
The energy to change the temperature of a mass is E = mcΔθ. c is the specific heat capacity: how many joules warm 1 kg by 1 °C. For water, c is 4 200 J/kg °C. A heater supplies energy at E = Pt, and if nothing escapes, the two expressions match.
Changing state at constant temperature takes energy too. E = mL, where L is the specific latent heat. That is why a kettle that has reached 100 °C keeps taking energy while the water turns to steam, without the temperature rising.
Formulas
Specific heat capacity
E = mcΔθ
A temperature change with no change of state. Δθ is in °C or K; the difference is the same.
- E
- energy
- J
- m
- mass
- kg
- c
- specific heat capacity
- J/kg °C
- Δθ
- temperature change
- °C
Specific latent heat
E = mL
Melting or boiling, with no temperature change. L is larger for vaporising than for melting.
- E
- energy
- J
- m
- mass that changes state
- kg
- L
- specific latent heat
- J/kg
Energy from a heater
E = Pt
Pair this with E = mcΔθ when a heater warms a substance and losses are ignored.
- E
- energy
- J
- P
- power
- W
- t
- time
- s
Worked examples
Warming water with a heater
0.20 kg of water is warmed from 20 °C to 100 °C. c = 4 200 J/kg °C. How much energy is needed, and how long does an 800 W heater take if no energy escapes?
- Mass
- 0.20 kg
- Temperature change
- 80 °C
- Heater
- 800 W
Try it on paper first. Then open the working one step at a time.
Melting ice at 0 °C
How much energy melts 0.050 kg of ice at 0 °C? The specific latent heat of fusion of ice is 3.34 × 10⁵ J/kg. The water produced is still at 0 °C.
- Mass
- 0.050 kg
- L
- 3.34 × 10⁵ J/kg
Try it on paper first. Then open the working one step at a time.
Checks
2.0 kg of aluminium (c = 900 J/kg °C) is warmed by 15 °C. How much energy is transferred, in joules?
2 100 J of energy warms some water by 1.0 °C. c = 4 200 J/kg °C. What is the mass of the water, in kg?
A 100 W heater runs for 40 s in 0.10 kg of water. c = 4 200 J/kg °C. Ignore losses. What is the temperature rise, to 1 decimal place, in °C?
Which statement is correct?
Easy places to lose a mark
- Using the final temperature instead of the change.
- Using E = mcΔθ while a substance is melting or boiling. The temperature is not changing.
- Forgetting that a real heater also warms the beaker and the air, so the liquid does not get all of Pt.
Practical
Heat can
Predict the temperature rise from a heater running for 60 s.