Specific heat capacity Cambridge International AS & A Level Physics revision
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In plain words
Some things warm up easily and others take a lot of heating. Water is stubborn: it takes about 4200 joules to warm one kilogram by a single degree, which is why the sea stays cool on a hot day. That number is water's specific heat capacity.
Three things to know
- The specific heat capacity c of a substance is the energy needed per unit mass to raise its temperature by one degree. ΔE = mcΔθ. Units: J kg⁻¹ K⁻¹.
- To measure it: heat a known mass with an electrical heater, and measure the energy supplied (VIt) and the rise in temperature. Then c = VIt ÷ mΔθ.
- Insulate the sample to cut down energy losses. Any energy that escapes makes the measured value of c too big.
Worked example
A 2.0 kW kettle heats 1.5 kg of water from 20 °C to 100 °C. The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹. Find the time it takes, assuming no energy is lost.
- ΔE = mcΔθ = 1.5 × 4200 × 80 = 504 000 J.
- Time = energy ÷ power = 504 000 ÷ 2000.
- = 252 s, a little over four minutes.
Tips and tricks
- Δθ is the change in temperature, not the final temperature.
- When hot and cold things are mixed, the energy lost by the hot one equals the energy gained by the cold one.
It lands in your notebook with its questions as flashcards.
Specific heat capacity: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is the specific heat capacity of a substance?
It is energy per unit mass per unit temperature rise.
What are the units of specific heat capacity?
From c = ΔE ÷ mΔθ.
The same energy is given to equal masses of X and Y. X has twice the specific heat capacity of Y. How does the temperature rise of X compare?
A bigger c means a smaller rise for the same energy.
How much energy is needed to raise the temperature of 2.0 kg of water by 10 K? (c = 4200 J kg⁻¹ K⁻¹.)
2.0 × 4200 × 10.
In an experiment to measure c, some energy escapes to the surroundings. How does this affect the result?
More energy is supplied than the sample actually receives.
Quiz
5 questions
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Worksheet
3 questions, 8 marks. Write your answers on paper, then check them.
Specific heat capacity
Cambridge International AS & A Level Physics 9702 · 8 marks · papermunch.org
Name ______________________________ Date ______________
Find the energy needed to raise the temperature of 0.50 kg of aluminium by 30 K. (c = 900 J kg⁻¹ K⁻¹.)[2]
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13 500 J.
A 50 W heater warms a 1.0 kg metal block for 200 s, and its temperature rises by 20 K. Find the specific heat capacity of the metal.[3]
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500 J kg⁻¹ K⁻¹. 10 000 J ÷ (1.0 × 20).
0.20 kg of water at 80 °C is mixed with 0.30 kg of water at 20 °C. Find the final temperature, assuming no energy is lost.[3]
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44 °C. 0.20 × (80 − T) = 0.30 × (T − 20).
Answers: Specific heat capacity
- 1. 13 500 J.
- 2. 500 J kg⁻¹ K⁻¹. 10 000 J ÷ (1.0 × 20).
- 3. 44 °C. 0.20 × (80 − T) = 0.30 × (T − 20).