Why does a graph showing the change in temperature as a substance is heated have flat sections to it?

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P3 F) Specific Latent Heat

Heating – Melting & BoilingWhen we heat a substance, we increase the amount of energy in the internal energy stores of the substance.If the temperature of a substance is not at its melting or boiling point, the energy that we put into the substance will increase the energy in the kinetic energy stores of the particles in the substance, which will result in the temperature of the substance increasing.  

When we put energy into a substance that is at its melting or boiling point, the energy that we put in is used to break the intermolecular bonds between the particles/ molecules in the substance rather than to increase the temperature of the substance. This leads to flat parts on a heating graph. A heating graph shows how the temperature of a substance changes as we add more heat/ energy to a substance; we heat up a substance for a certain period of time and see how the temperature changes. An example of a heating graph is shown below.

The x axis for heating graphs is time and the y axis is temperature. The x axis for a heating graph is essentially energy and for the heating of a substance, the left part of the x axis is little energy and the right part of the x axis is lots of energy.On the 3 upwards sloping parts of the graph, the energy from heating the substance goes to the kinetic energy stores of the particles in the substance, which causes the temperature of the substance to increase within a state. From left to right, the states on the upwards sloping parts of the graph are solid, liquid and gas.When the substance reaches its melting or boiling point, the energy from heating is used to break the intermolecular bonds between the particles in the substance, which results in a change in state; the energy from heating goes to increasing the potential energy stores of the particles rather than the kinetic energy stores of the particles. This is why the temperature of the substance during a change in state remains the same, hence the flat parts on the graph. The first flat part from the left is melting (solid to liquid) and the second flat part is evaporating or boiling (liquid to gas).I am now going to look at heating water in a kettle to get the water to 100°C. When the water in a kettle reaches 100°C, the majority of the water stays as a liquid rather than all of the water turning into a gas. The majority of the water stays as a liquid because more energy would be required from the kettle to break the intermolecular bonds in the liquid water for it to change from a liquid to a gas. The heating of water in a kettle gets the water to the start of the boiling flat part.  

Cooling – Condensing & FreezingThe heating graph for the cooling of a substance is shown below.

The x axis for the heating graph is time, which is essentially energy. For this graph, we are cooling a substance so the left part of the x axis is lots of energy and the right part of the x axis is little energy.On the 3 downwards sloping parts of the graph, the particles are losing energy from their kinetic energy stores, which results in the temperature of the substance decreasing within a state. From left to right, the states on the downwards sloping parts of the graph are gas, liquid and solid.Intermolecular bonds form when a substance condenses (gas to liquid) or freezes (liquid to solid). The forming of intermolecular bonds releases energy. This means that when a substance is at its condensing or freezing point, the internal energy of the substance decreases, but the temperature of the substance does not change because the intermolecular bonds that form release energy. This leads to flat parts on the graph where the substance is condensing and freezing. The first flat part on the left is condensing and the second flat part is freezing.

Specific Latent Heat for a Change of StateThe specific latent heat is the amount of energy that is needed to change the state of 1 kg of a substance without changing the temperature of the substance (it is the amount of energy that has been used/ given off for the flat parts on both of the above graphs if the graph was for 1 kg of a substance). The specific latent heat is different for different substances and this is because different substances have different strengths for their intermolecular bonds.

There are two specific latent heats. These are:

1. Specific latent heat of fusion – the amount of energy that is needed to melt 1 kg of a substance at its melting point. Or, it is the amount of energy that is given off when 1 kg of a substance freezes at its freezing point.
2. Specific latent heat of vaporisation – the amount of energy that is needed to evaporate/ boil 1 kg of a substance at its boiling point. Or, it is the amount of energy that is given off when 1 kg of a substance condenses at its condensing point.

We are able to work out the amount of energy needed to change the state of a certain mass of a substance by using the formula below:

Energy in the above formula is measured in kJ, mass is measured in kg and SLH is measured in kJ/kg. Whenever we are using this formula, we need to make sure that the units for the values are correct.If we are working out the amount of energy needed to change a solid to a liquid at its melting point (or vice versa), SLH in the above formula would be the specific latent heat of fusion. If we are working out the amount of energy needed to change a liquid to a gas at its boiling point (or vice versa), SLH in the above formula would be the specific latent heat of vaporisation. We need to make sure that we use the correct SLH because the values for SLH of fusion and SLH of vaporisation are different (you can see this from looking at the table).

​Let’s have a few examples.

Example 13.2 kilograms of lead is at its boiling point. How much energy is needed to change the 3.2 kilograms of lead from a liquid to a gas? The specific latent heat of vaporisation for lead is 885 kJ/kg.We can work out the amount of energy required by multiplying the mass by the SLH of vaporisation for lead.

In the formula, mass needs to be in kilograms which it is (3.2 kg), and L or SLH needs to be in kJ/kg which it is (885 Kj/kg). Everything is in the correct units, so we just put the values into the calculation; we put mass in as 3.2 and the SLH as 885.

​This tells us that it takes 2,832 kJ to change 3.2 kg of lead from a liquid to a gas.

Example 2How much energy is needed to change 500 grams of ice from a solid to a liquid at a temperature of 0°C? Give your answer in kJ. The specific latent heat of fusion for water is 334 kJ/kg.​The question tells us that the ice is at a temperature of 0°C, which means that the ice is at its melting point. Therefore, we find the amount of energy needed to change the 500 grams of water from a solid to a liquid by multiplying the mass by the SLH of fuison for water.

The mass in the formula above needs to be in kilograms; currently the mass is in grams (500g). 1 kilogram is 1000 g, so we can convert grams to kilograms by dividing by 1000. Therefore, the mass in kilograms is 0.5 kg (500 ÷ 1000 = 0.5). The question tells us that the specific latent heat of fusion for water is 334 kJ/kg, which is in the correct units. We now have everything that we need for the calculation in the correct units; we sub the mass in as 0.5 and the SLH as 334.

​This tells us that it takes 167 kJ of energy in order to change 500 grams of water from a solid to a liquid when the water is at its melting point.