Specific heat capacity · Grade 12
In Grade 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
- 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 1.5 kW heater warms a 2.0 kg aluminum block for 2 minutes. The temperature rises by 90°C. Find c for aluminum (assume no losses).
Answer: 1,000 J/(kg °C)
Example 2
A 50 W heater warms a 1.0 kg aluminum 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 3
A student measures the specific heat capacity of aluminum 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 4
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