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

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1. How much work would it take to heat 100kg 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 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:

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.