A-level Physics (Advancing Physics)/Specific Heat Capacity/Worked Solutions

1. How much work would it take to heat 100 kg of liquid water from 20 °C to 36.8 °C?

$$\Delta E = mc \Delta \theta = 100 \times 4180 \times 16.8 = 7.022\mbox{ MJ}$$

2. How much work would it take to heat a well-insulated room from 15 °C to 21 °C, if the room is a cube with side length 10m, and the density of the air is 1.2kgm−3?

$$V = 10^3 = 1000\mbox{ m}^3$$

$$\rho = \frac{m}{V}$$

$$m = V\rho = 1000 \times 1.2 = 1200\mbox{ kg}$$

$$\Delta E = mc \Delta \theta = 1200 \times 1010 \times 6 = 7.272\mbox{ MJ}$$

'''3. A 10 kg block of iron at 80 °C is placed in the room above once it has reached 21 °C. If the iron cools by 40 °C, what is the new temperature of the room?'''

Energy must be conserved, so:

$$10 \times 450 \times 40 = 1200 \times 1010 \times \Delta \theta$$

$$\Delta \theta = \frac{180000}{1212000} = 0.149$$°C

So, the new temperature of the room is 21.149 °C.