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

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

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

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?

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

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

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

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

3. A 10kg 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:

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

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

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