Specific heat capacity · Year 12
In Year 12 you learn: mixing hot and cold.
The specific heat capacity of a material is the energy needed to warm 1 kg of it by 1°C. Water needs a lot, 4,200 J for each kilogram and degree, while metals need much less. The energy to change the temperature of anything is E = mcΔT, and you can measure c by heating a block with an electric heater.
Key facts
- Energy to change temperature: E = mcΔT (c = specific heat capacity, J/kg °C).
- Water: c = 4,200 J/kg °C, much higher than most substances.
- To measure c, heat a block with an electric heater: c = E ÷ (mΔT). Energy lost to the surroundings makes the result too high.
- When hot and cold mix: energy lost by the hot = energy gained by the cold.
Worked examples
Example 1
A cup of milk is heated from 17°C to 60°C. What is the temperature change?
Answer: 43 °C
Example 2
How much energy heats 2.0 kg of water from 20°C to 70°C?
Answer: 420,000 J
Example 3
What temperature rise does 21,000 J of energy give 0.50 kg of water? (c = 4,200 J/kg°C)
Answer: 10°C
Example 4
1.0 kg of water and 1.0 kg of copper are each given 4,000 J. Which warms up more, and by how much? (water: 4,200 J/kg°C; copper: 385 J/kg°C)
Answer: the copper: about 10.4°C, against about 0.95°C for the water
Example 5
A 1.5 kW heater warms a 2.0 kg aluminium block for 2 minutes. The temperature rises by 90°C. Find c for aluminium (assume no losses).
Answer: 1,000 J/(kg °C)
Example 6
A 50 W heater warms a 1.0 kg aluminium block for 300 s, and its temperature rises by 16°C. Find the specific heat capacity it measures. Why is it more than the true value, 900 J/kg°C?
Answer: about 940 J/kg°C; some energy heats the surroundings instead of the block
Example 7
A student measures the specific heat capacity of aluminium as 1,050 J/kg °C, higher than the true value of 900. What is the most likely reason?
Answer: energy was lost to the surroundings, so more energy was measured than actually heated the block
Example 8
A 3,000 W kettle is 93% efficient. How long does it take to heat 1.1 kg of water from 16°C to 100°C? Give your answer to the nearest second. (c of water = 4,200 J/kg °C.)
Answer: 139 s
Example 9
0.5 kg of water at 83°C is mixed with 0.7 kg of water at 16°C in an insulated jug. What is the final temperature, to 1 decimal place?
Answer: 43.9°C