phy 問題about heat

When the cooling system is working, the cooling system can use the heat energy to heat up the water.

E=mc(dt)

Energy required for heating up 1 kg water from 15c to 95 c:
=1 * 4200 * (95-15) = 336000J
Power in the engine is 336000Js-1 = 336000W

If the cooling system is failed, those all the energy for heating up the water would be used to heat up the engine instead of the water.

Power = Energy / Time (rearrange the formulae)
Time = Energy / Power

Time = Energy required to heat up the engine from 15c to 200c / Power

200 * 450 * (200-15) = 336000* time
time = 16650000 / 336000 = 49.55s

Time taken for the engine to overheat from 15c to 200c is approximately 50s.
It's because that the energy needed to heat up the water would be used to heat up the engine when the cooling system failed. The energy that water gain should equal to the energy generated by the engine. Therefore, I used the power of the engine to calculate the time needed to overheat the engine.

energy needed to heat the steel engine from 15c to 200c
(c=digree c)
450x200x(200-15)
=15750000J

energy absorbed by water from engine per second(assume no energy loss to the surroundings)
4200x1x(95-15)
=336000J

time need to heat the engine if the system is failed
15750000/336000
=46.875s