Coal releases heat.
Ice gains heat and undergo change of state. So heat gained is used to raise temperature of ice from -10oC to 0oC, to undergo change of state from ice to water as well as to raise temperature of water from 0oC to final temperature.
Let final temperature be θ.
heat lost by coal = heat gained by ice + heat gained to change state + heat gained by water
mc cc ∆θc = mi ci ∆θi + m lf + mw cw ∆θw
0.05 * 710 * (200 – θ) = 0.01 * 2100 * (0 – (-10)) + 0.01 * 336000 + 0.01 * 4200 * (θ-0)
θ = 46.1oC
Using the formula Pt = (4.2 × L × T ) ÷ 3600 you can calculate the time it takes to heat a specific quantity of water from one temperature to another temperature.
Calculate the kilowatt-hours (kWh) required to heat the water using the following formula: Pt = (4.2 × L × T ) ÷ 3600. Pt is the power used to heat the water, in kWh. L is the number of liters of water that is being heated and T is the difference in temperature from what you started with, listed in degrees Celsius.
Substitute in the appropriate numbers into the equation. So imagine you are heating 20 liters of water from 20 degrees to 100 degrees. Your formula would then look like this: Pt = (4.2 × 20 × (100-20)) ÷ 3600, or Pt = 1.867
Calculate the amount of time it takes to heat the water by dividing the power used to heat the water, which was determined to be 1.867 with the heater element rating, listed in kW. So if your heater element rating was 3.6 kW, your equation would look like this: heating time = 1.867 ÷ 3.6, or heating time =0.52 hours. Therefore, it would take 0.52 hours to heat 20 liters of water, with an element with a rating of 3.6 kW.