This topic accounts for approximately 6% of your exam marks.
stable
Low
Stable6%
Specific heat capacity, specific latent heat and heating/cooling curves tested consistently.
Definition
The (c) of a substance is the amount of energy needed to raise the temperature of 1 kg of the substance by 1 °C
The SI unit is joules per kilogram per degree Celsius (J/(kg °C)) (equivalent to J/(kg K) since temperature differences are the same in °C and K)
Reference values for a feel:
water: 4200 J/(kg °C), very high, which is why oceans moderate climate and water-cooled radiators work
aluminium: 900 J/(kg °C)
copper: 385 J/(kg °C)
iron: 460 J/(kg °C)
air: 1000 J/(kg °C)
Implications of high vs low c
A substance with a high specific heat capacity:
heats up slowly for a given energy input
cools down slowly when energy is removed
is good for storage heaters, hot-water bottles and household central-heating systems (water carries lots of heat per kilogram)
A substance with a low specific heat capacity:
heats up quickly and cools down quickly
is good for cooking pans and engine pistons (metals heat fast, conduct fast, cool fast)
The energy equation
ΔQ = m × c × ΔT
where:
ΔQ = energy supplied to (or removed from) the substance (J)
m = mass of the substance (kg)
c = specific heat capacity (J/(kg °C))
ΔT = change in temperature (°C)
This equation only applies while the substance is not changing state. During a change of state, the temperature does not change so ΔT = 0 and the equation gives zero, but real energy is still being delivered (into the potential store)
Worked example
Calculating thermal energy using ΔQ = m × c × ΔT
A 2.0 kg iron pan is heated from 20 °C to 120 °C. The specific heat capacity of iron is 460 J/(kg °C). Calculate the thermal energy transferred to the pan.
Solution:
Identify the temperature change: ΔT = 120 − 20 = 100 °C
Write the equation: ΔQ = m × c × ΔT
Substitute: ΔQ = 2.0 × 460 × 100
= 92 000 J
Exam tip
Rearranging ΔQ = m × c × ΔT when a different quantity is unknown
What comes up: a calculation where mass or specific heat capacity is the unknown (the energy and temperature change are given). Worth 3 marks.
Write (three marks): (1) substitute the known values into ΔQ = m × c × ΔT in the correct positions; (2) rearrange to make the unknown the subject; (3) evaluate to at least 2 significant figures.
Watch out: always calculate ΔT as a subtraction before substituting — if you use the final temperature alone instead of the change, you lose the ΔT mark. The mark scheme awards the rearrangement mark separately, so show it as a distinct line of working even if you can do it in your head.