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.