When solving problems involving specific heat capacities, you only need to know two equations!
1. Heat = mass × specific heat capacity × temperature change
Q = mc Dq
and
2. Heat lost = Heat gained
mc Dq = mc Dq
When reading the question, concentrate on what is losing heat and what is gaining heat - then use the above two equations to solve the problem.
Question 1
Given that the specific heat capacity of water is 11 times that of copper, calculate the mass of copper at a temperature of 100 °C required to raise the temperature of 200 g of water from 20.0 °C to 24.0 °C, assuming no energy is lost to the surroundings.
Solution
Heat lost by copper = heat gained by water
mcuccuDqcu = mwcwDqw
mcuccu(100 - 24) = 0.200 × 11ccu(24 – 20)
76mcu = 8.8
mcu = 0.116 kg
Question 2
Three litres of water at 100 °C are added to 15 litres of water at 40 °C. Calculate the temperature of the mixture. Take the mass of 1 litre of water to be 1 kg and the specific heat capacity of water to be 4.2 × 103 J kg -1 K -1
Solution
Let the temperature of the mixture q
Heat lost = heat gained
m1c1Dq1 = m2 c2 Dq2
3 × 4.2 × 103 × (100 – q) = 15 × 4.2 × 103 × (q -40)
Solving for q gives q = 50°C
You try it!
Question 3
1 kg of water at a temperature of 45 °C is mixed with 1.5 kg of alcohol at 20 °C. Find the final temperature of the mixture.
Take the specific heat capacity of water to be 4200 J kg –1 K –1 and the specific heat capacity of alcohol to be 2400 J kg –1 K –1 . Assume no other exchange of heat occurs.
Solution
Let the final temperature of the mixture be q.
Heat lost by water = heat gained by alcohol
mwcwDqw = malcalDqal
1 × 4200 × (45 – q) = 1.5 × 2400 × (q – 20)
(mcDq)w = (mcDq)al
1 × 4200 × (45 – q) = 1.5 × 2400 × (q – 20)
Solving for q gives q = 33 °C.
You try it!
Some electrical heaters contain oil which has a high boiling point and a relatively high specific heat capacity. Once the oil has been heated it retains the thermal energy for quite a while, cooling down only slowly.
In storage heaters, a core of high-density thermal blocks (like very hard building blocks), is heated by electric elements during the night. These blocks are preferred to water, despite having a slightly lower specific heat capacity, because they are more dense (and thus more compact) and do not leak. They are heated during the night using low-cost (off-peak) electricity and release the stored thermal energy during the day.
Storage heaters maintain a steady room air temperature over long periods, warming the entire building fabric and reducing the risk of condensation.
Next: Learn It - Experiment 1