How much coal needs to be burned to heat 200 g water from 0 ° C to 100 ° C.

Water mass m1 = 200 g = 0.2 kg

Initial water temperature t0 = 0 0С

Final water temperature t = 100 0С

Specific heat capacity of water c = 4200 J / kg * ºС

Specific heat of combustion of coal q = 2.7 * 10 ^ 7 J / kg

m2 is the mass of coal.

The heat from burning coal is used to heat water. If there is no heat loss, then you can write

m2 * q = m1 * c * (t – t0)

Hence m2 = m1 * c * (t – t0) / q

m2 = 0.2 kg * 4200 J / kg ºС * (100 0С – 0 0С) / 2.7 * 10 ^ 7 J / kg

m2 ≈ 0.003 kg = 3g

Answer: you need 3 g of coal