Specific heat capacityIB MYP Physics: Revision notes
Section 1
What is specific heat capacity?
When a substance is heated, its particles gain kinetic energy and its temperature rises. But different materials need different amounts of energy to warm up by the same amount.
The specific heat capacity of a substance is the energy needed to raise the temperature of 1 kg of the substance by 1 °C. Its unit is J/kg °C.
Water has a very high specific heat capacity of about 4200 J/kg °C, so it takes a lot of energy to heat it up and it stays warm for a long time. Aluminium is about 900 J/kg °C and copper about 380 J/kg °C, so metals heat up and cool down quickly. This is why sand on a beach is burning hot by afternoon while the sea stays cool.
Specific heat capacity is not the same as heat capacity. It is always 'per kilogram', so its unit is J/kg °C, not J/°C.
Section 2
The equation Q = m c ΔT
The energy transferred to change the temperature of a substance is
Q = m × c × ΔT
- Q = energy transferred in joules (J)
- m = mass in kilograms (kg)
- c = specific heat capacity in J/kg °C
- ΔT = change in temperature in °C (final temperature − starting temperature)
Rearranged: c = Q ÷ (m ΔT), and ΔT = Q ÷ (m c). A bigger mass, a bigger specific heat capacity or a bigger temperature change all mean more energy is needed.
ΔT is the change in temperature, not the final temperature. Heating water from 20 °C to 100 °C gives ΔT = 80 °C, not 100 °C. Also convert grams to kilograms first.
Section 3
Worked examples
Energy needed. How much energy is needed to heat 2.0 kg of water from 20 °C to 70 °C? (c = 4200 J/kg °C)
ΔT = 70 − 20 = 50 °C Q = m c ΔT = 2.0 × 4200 × 50 = 420 000 J
Temperature rise. A 0.50 kg block of water receives 8400 J of energy. How much does its temperature rise?
ΔT = Q ÷ (m c) = 8400 ÷ (0.50 × 4200) = 8400 ÷ 2100 = 4.0 °C
Write down Q, m, c and ΔT with units, then rearrange before substituting numbers. Check that your answer is sensible: a small mass and a small energy should not give a huge temperature change.
Section 4
Electrical heating experiments
To measure c, we heat a solid block of known mass with an electric immersion heater and measure the temperature rise.
The energy transferred by the heater is E = P t (power × time) or, with a current and voltage, E = I V t. For example, a 50 W heater running for 200 s transfers 50 × 200 = 10 000 J.
Method: measure the mass of the block, record the starting temperature, switch on the heater for a measured time while recording the current and voltage, then record the highest temperature. Then calculate c = I V t ÷ (m ΔT).
A small amount of oil in the thermometer hole helps the temperature reading to be accurate.
Section 5
Heat loss and improving the experiment
Not all of the electrical energy ends up in the block. Some is transferred to the surroundings by conduction, convection and radiation, and some heats the thermometer and heater. The block therefore warms by less than it should.
Because c = Q ÷ (m ΔT), a ΔT that is too small makes the calculated value of c too high.
Ways to reduce the error:
- wrap the block in insulation (lagging) or use a lid
- use a little oil to improve thermal contact with the thermometer
- repeat the experiment and take a mean
In an evaluation, link the cause to its effect: heat loss, so a smaller temperature rise, so a calculated c that is too high.
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Specific heat capacity
- On a sunny afternoon in Dubai, the sand on a beach becomes too hot to walk on, while the sea water beside it feels pleasantly cool. Each kilogram of sand and each kilogram of sea water absorbs about the same amount of energy from the Sun.Explain why the temperature of the sand rises by much more than the temperature of the sea water.2 marks
- An electric kettle contains 1.5 kg of water at 20 °C. The heating element has a power of 2000 W. The specific heat capacity of water is 4200 J/kg °C, and the water must reach 100 °C to boil.In practice the kettle takes longer than the time calculated. Explain why.2 marks
- A student measures the specific heat capacity of aluminium using a block of mass 1.00 kg. The block has two holes: one holds a 12 V electric heater and the other holds a thermometer. The heater carries a current of 5.0 A for 300 s. The block is not insulated, and its temperature rises from 20.0 °C to 39.0 °C.Calculate the specific heat capacity of aluminium from the student's results. Give your answer to three significant figures.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).