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?

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

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?

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

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

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

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

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:

$10\times 450\times 40=1200\times 1010\times \mathrm{\Delta }\theta$

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

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