Heating water in a container
When water is heated in a container, the container heats up too, and it needs heat of its own.
Example 4
1 kg of water at 25 °C is in a copper vessel; the vessel and water together have a mass of 1.6 kg. How much heat is needed to bring the water to the boil? (water: 4200 J kg-1 K-1; copper: 400 J kg-1 K-1)
Total heat = heat taken by the vessel + heat taken by the water
Mass of the vessel = 1.6 kg − 1.0 kg = 0.6 kg
Vessel: 0.6 × 400 × (100 − 25) = 18 000 J
Water: 1 × 4200 × (100 − 25) = 315 000 J
Total = 333 000 J
Exercise 9.2
The questions
- Iron has c = 460 J kg-1 K-1. Find the heat needed to raise 2 kg of iron from 25 °C to 65 °C.
- 0.8 kg of aluminium at 30 °C is given 14 400 J (c = 900 J kg-1 K-1). Find its temperature.
- A 500 g glass vessel holds 400 g of water at 25 °C. Find the heat needed to bring the water to the boil. (glass: 840 J kg-1 K-1; water: 4200 J kg-1 °C-1)
The answer
- Q = 2 × 460 × (65 − 25) = 36 800 J
- θ = 14 400 ÷ (0.8 × 900) = 20 °C, so the temperature becomes 30 + 20 = 50 °C
- Glass: 0.5 × 840 × 75 = 31 500 J; water: 0.4 × 4200 × 75 = 126 000 J; total 157 500 J