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Example 2 Question : How much heat is required to evaporate 5 kg of water at 100 ° C ? The “ heat of evaporation ” for water at 100 ° C is 2257 kJ / kg .
Answer : The latent heat formula is : Q = m · h f g The amount of heat required = 5 X 2257 = 11 285kJ .
Example 3 Question : The geyser at your home contains 200 litres of water and the element installed has a capacity of 3 kW . How long will it take to heat the water from 20 ° C to 70 ° C ?
Answer : The amount of heat required to heat the water can be calculated from the sensible heat formula . Thus : Q = m · c · ∆T = 200 X 4,2 X ( 70 – 20 ) = 42 000kJ .
The heat is added at a rate of 3 kJ / s \ the time taken to heat the water is therefore : 42 000 ÷ 3 = 14 000 seconds . 14 000 ÷ 60 = 233 minutes which is 3 hours and 53 minutes ( rounded off ).
Example 4 Question : A hot water storage tank in a large building holds 15 000 litres of water . This water must be heated up from 40 ° C to 85 ° C during the night .
The electrical energy will be available from 10:00PM to 05:00AM . Calculate the capacity of the electric heaters required . The specific heat of water is 4,2 kJ / kg and 1 litre is equivalent to 1 kg .
Answer : The amount of heat required to heat the water is calculated from the sensible heat formula . Thus the amount of heat required is : mc∆T = 15 000 X 4,2 X ( 85 – 40 ) = 2835 000kJ . This amount of heat is required and is independent of the amount of time available .
The capacity of the heater elements is given in Joules per second ( J / s ). Thus the amount of heat to be added per second must be calculated . The time available is 7 hours which is 7 x 3600 seconds = 25200 seconds . The amount of heat to be added per second = 2 835 000 ÷ 25 200 = 112,5 kJ / s .
As 1kW = 1kJ / s the capacity of the heater must be 112,5kW .
Often calculations involve both sensible and latent heat . Examples of this include the humidification of air and the production of ice . When doing calculations involving both sensible and latent heat you must be very careful to determine which is sensible heat and which is latent heat .
Remember : Sensible heat is what changes the temperature of a substance without changing its phase . Latent heat changes the phase without changing the temperature .
If you put a pot of water with ice blocks in it on the stove and switch the stove on heat will be added . Initially this heat will be
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RACA Journal I September 2022 www . refrigerationandaircon . co . za