Further sensible heat energy will then be needed to raise its temperature to boiling point, followed by more latent heat (of vaporization) to change it into steam. See Figure 2.1.2.
Figure 2.1.2 Sensible and latent heat
Just as each substance has its own value of specific heat, so each substance has a value of latent heat of fusion and latent heat of vaporization.
The latent heat of fusion of ice is 335 kJ/kg, that is, it needs 335 kJ for each kg to change it from ice to water. Note that there is no temperature term in the unit because, as we have already seen, no temperature change occurs. Compare this with the unit for specific heat (kJ/kgK).
The latent heat of vaporization of water at atmospheric pressure is 2256.7 kJ/kg. If instead of boiling the water, we are condensing it, we would need to extract (in a condenser) 2256.7 kJ/kg. The values vary with pressure.
The significance of this theory cannot be underestimated, since it relates directly to steam plant and refrigeration plant, both of which we look at later.
Example 2.1.5
Calculate the heat energy required to change 4 kg of ice at −10°C to steam at atmospheric pressure.
Specific heat of ice = 2.04 kJ/kgK
Latent heat of fusion of ice = 335 kJ/kg
Specific heat of water = 4.2 kJ/kgK
Latent heat of vaporization of water = 2256.7 kJ/kg
Referring to Figure 2.1.2 we can see that all we have to do is add four values together, i.e. the heat energy to raise the temperature of the ice to 0°C, to turn the ice into water, to raise the water to 100°C, and to change the water at 100°C into steam.
To change the ice at 0°C into water at 0°C,
To change the water into steam at 100°C,
In this example, we could provide the 12 128.4 kJ very quickly with a large kW heater, or much more slowly with a small kW heater. Neglecting losses, the result would be the same, i.e. steam would be produced.
As an exercise, and referring to the earlier example of the kettle, find how long it would take to produce the steam in Example 2.1.5 if you used a 2 kW heater and then a 7 kW heater, neglecting losses.
You will notice that we have dealt here mainly with water, since this is by far the most important substance with which engineers must deal. The theory concerning the heating of water to produce steam is the same as for the heating of liquid refrigerant in a refrigeration plant.
Problems 2.1.2
(1) Calculate the quantity of heat energy which must be transferred to 2.25 kg of brass to raise its temperature from 20°C to 240°C if the specific heat of brass is 394 J/kgK.
(2) Find the change in temperature produced by 10 kJ of heat energy added to 500 g of copper. Specific heat of copper = 0.39 kJ/kgK.
(3) Explain why, for a gas, the specific heat at constant volume has a different value from the specific heat at constant pressure.
An ideal gas is contained in a cylinder fitted with a piston. Initially the temperature of the gas is 15°C. If the mass of the gas is 0.035 kg, calculate the quantity of heat energy required to raise the temperature of the gas to 150°C when:
(b) the piston moves and the pressure is constant.
For the gas, cv = 676 J/kgK and cp = 952 J/kgK.
(4) 2 kg of ice at −10°C is heated until it has melted. How much heat energy has been used? Specific heat of ice = 2.1 × 103 J/kgK. Latent heat of fusion of ice = 335 kJ/kg.
(5) Calculate the heat energy required to melt 6 kg of lead at 20°C.
Latent heat of fusion of lead = 24.7 kJ/kg.
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