CHAPTER 16 Latent Heat Capacity The use of an equation

Definition When a solid is heated, it may melt and change its state from solid to liquid. If ice is heated it becomes water. The opposite process of freezing occurs when a liquid solidifies. A pure substance melts at a definite temperature, called the melting point; it solidifies at the same temperature - the freezing point.

Experiment: cooling curve of ethanamide Half-fill a test-tube with ethanamide (acetamide) and place it in a beaker of water. Heat the water until all the ethanamide has melted.

Remove the test-tube and arrange it as in figure with a thermometer in the liquid ethanamide. Record the temperature every minute until it has fallen to 70oC. Plot a cooling curve of temperature against time. What is the freezing (melting) point of ethanamide?

Types of latent heat There exists two types of latent heat. This occurs when solids becomes liquids or vice-versa and is called specific latent heat of fusion. This occurs when liquids becomes gases or vice-versa and is called specific latent heat of vaporization.

Latent heat of fusion The previous experiment shows that the temperature of liquid ethanamide falls until it starts to solidify (at 82oC) and remains constant till it has all solidified. The cooling curve in the following figure is for a pure substance; The flat part AB occurs at the melting point when the substance is solidifying. During solidification a substance loses heat to its surroundings but its temperature does not fall.

Conversely when a solid is melting, the heat supplied does not cause a temperature rise. For example, the temperature of a well-stirred ice-water mixture remains at 0oC until all the ice is melted.

Heat which is absorbed by a solid during melting or given out by a liquid during solidification is called latent heat of fusion. Latent means hidden and fusion means melting. Latent heat does not cause a temperature change; it seems to disappear. The specific latent heat of fusion of a substance is the quantity of heat needed to change unit mass from solid to liquid without temperature change. It is measured in J/kg or J/g.

The latent heat equation In general, we can write the ‘latent heat equation’ as i.e. E = mL Note that this equation does not depend on temperature since there is no temperature change during the latent heat. Heat received or given out = mass × Latent Heat Capacity

Latent heat graph of water

Experiment: specific latent heat of fusion of ice Place a 12V electric immersion heater of known power in a filter funnel and pack small pieces of ice round it. Switch on the heater for 3 minutes and find the mass of water which collects in a beaker.

Experiment: specific latent heat of fusion of ice Arrange the results as shown. Power of immersion heater = W(J/s) Time heat supplied = s  Heat supplied to ice = J Mass of beaker empty = g Mass of beaker + melted ice = g Mass of melted ice = g Calculate the heat needed to melt 1g of ice. What are causes of error in this experiment?

Latent heat of vaporization Latent heat is also needed to change a liquid into a vapour. The reading of a thermometer in boiling water remains constant at 100oC even though heat, called latent heat of vaporization, is still being absorbed by the water from whatever is heating it. When steam condenses to form water, latent heat is given out. This is why a scald from steam may be more serious than one from boiling water.

The specific latent heat of vaporization of a substance is the quantity of heat needed to change unit mass from liquid to vapour without change of temperature.

Table 1 The following table gives the Latent heat capacity of some common substances. Note carefully the units of the latent heat. They are J/g or J g-1 If you want to change them to kilograms, just multiply by 1000. Ex. 334 J g-1 = 334 × 1000 = 334 000 J kg-1

Specific latent heat of fusion J.g-1 oC Substance Specific latent heat of fusion J.g-1 oC Specific latent heat of vaporization J.g-1 Water 334 2258 100 Ethanol 109 -114 838 78 Ethanoic acid 192 17 395 118 Chloroform 74 -64 254 62 Mercury 11 -39 294 357 Sulphur 54 115 1406 445 Hydrogen 60 -259 449 -253 Oxygen 14 -219 213 -183 Nitrogen 25 -210 199 -196

Example 1 How much heat is needed to change 20g of ice at 0oC to water at 0oC? Answer: Since here we have only a change of state then we are going to use the formula of latent heat of fusion (because it is ice). i.e. E = mL Latent heat of fusion of water = 334 Jg-1 So E = 20 × 334 = 6680 J

Example 2 How much heat is needed to change 50 g of mercury from liquid at 357oC to gas at 357oC ? Answer: Again we are going to use the Latent heat equation since this involves only a change of state. Latent heat of vaporization of mercury = 294 J/g E = 50 × 294 = 14700 J

Example 3 How much heat is needed to change 50 g of ice at 0oC to water at 10oC? Answer: This time we have to find the heat needed to change 50g of ice at 0oC to water at 0oC by using the latent heat equation. Then we have to find the heat needed to change 50g of water at 0oC to water at 10oC by using the specific heat capacity.

1) Latent heat of fusion of water = 334 J/g E = mL = 50 × 334 = 16700 J 2) Specific heat capacity of water = 4200J/kgoC Change to grams = 4200  1000 = 4.2J/goC To change from 0oC to 10oC E = mcT = 50 × 4.2 × 10 = 2100 J Total Energy = 16700 J + 2100 J = 18800 J

Exercise 1 How much heat is needed to change 250 g of Ethanol from solid at -114oC to liquid at -114oC? Ans: 27250 J How much heat is needed to change 335 g of water at 50oC to steam at 100oC? Ans: ES = 70350 EL = 756430 ET = 826780 J