Internal Energy
Energy is stored inside a system by the particles (atoms and molecules) that make up the system. This is called internal energy.
Internal energy is the total kinetic energy and potential energy of all the particles (atoms and molecules) that make up a system.
Unit: Joule
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Heating changes the energy stored within the system by increasing the energy of the particles that make up the system. This either :
- raises the temperature of the system or
- produces a change of state.
The specific heat capacity of a substance is the amount of energy required to raise the temperature of one kilogram of the substance by one degree Celsius.
Unit: J/kg°C
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If the temperature of the system increases, the increase in temperature depends on the mass of the substance heated, the type of material and the energy input to the system.
change in thermal energy = mass × specific heat capacity × temperature change
Question: The mass of water each cup is 200 g.
Calculate the energy, in joules, transferred from the water in a cup when the temperature of the water falls by 8°C.
Specific heat capacity of water = 4200 J / kg°C.
change in thermal energy = mass × specific heat capacity × temperature change
change in thermal energy = 0.2 x 4200 x 8
The energy transferred is 6720 Joules
Question: A student places 0.5 kg of potato into a pan of water.
During cooking, the temperature of the potato increases from 20 °C to 100 °C
The specific heat capacity of the potato is 3400 J/kg °C
Calculate the change in thermal energy of the potato
change in thermal energy = mass × specific heat capacity × temperature change
Change in temperature of potato = 100 – 20 = 80°C
change in thermal energy = 0.5 x 3400 x 80
The change in thermal energy is 136000 Joules
If a change of state happens the energy needed for a substance to change state is called latent heat.
When a change of state occurs, the energy supplied changes the energy stored (internal energy) but not the temperature.
The specific latent heat of a substance is the amount of energy required to change the state of one kilogram of the substance with no change in temperature.
Unit: J/kg
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When a substance is melting/freezing: use the specific latent heat of fusion
When a substance is condensing/evaporating: use the specific latent heat of vaporisation
The energy needed to change the state of a substance can be calculate using:
energy for a change of state = mass × specific latent heat
Question: While a kettle boils, 0.018 kg of water changes to steam.
Calculate the amount of energy required for this change.
Specific latent heat of vaporisation of water = 2.3 × 106 J / kg.
energy for a change of state = mass × specific latent heat
energy for a change of state = 0.018 x 2.3 × 106
The energy needed for the change of state = 41000 or 4.1 × 104 Joules
Question: A sample of air contained water that froze at 0 °C
The change in internal energy of the water as it froze was 0.70 kJ
The specific latent heat of fusion of water is 330 kJ/kg
Calculate the mass of ice produced.
energy for a change of state = mass × specific latent heat
700 = mass x 330000
mass = 700 / 330000
The mass of ice produced is 0.0021kg
Sometimes a question might involve both a change of state and then a change of temperature. You will need to think about the energy needed to to both of these things separately.
Question: The initial temperature of a mixture was +20 °C. The mixture froze at –1.5 °C.
A total of 165 kJ of internal energy was transferred from the mixture to cool and freeze it.
specific heat capacity of the mixture = 3500 J/kg °C
specific latent heat of fusion of the mixture = 255 000 J/kg
Calculate the mass of the mixture.
Give your answer to 2 significant figures.
Step 1: Work out the temperature change from +20 °C to –1.5 °C.
change in temperature = 20 – (-1.5) = 21.5 °C
total energy supplied = energy needed to cool the gas + energy needed to change the state of the gas
165000 = (mass × specific heat capacity × temperature change ) + (mass × specific latent heat)
165000 = (mass x 3500 x 21.5) + (mass x 255000)
165000 = 75250 x mass +255000 x mass
16500 = 330250 x mass
mass = 16500 / 330250
The mass is 0.049962kg = 0.050kg to 2sf
Cooling/Heating Curves
The heating curve shows how the temperature of a substance changes as energy is supplied to it.
Flat Lines: The substance is changing state. There is no temperature increase. All energy supplied is changing the internal energy not the temperature
Slanted Lines: The substance is changing temperature.
Question: Energy is transferred to the water in Figure 2 at a constant rate.
Explain why the graph is a different shape in parts A and B.
- in part A the increase in internal energy raises the temperature of the water
- in part B the increase in internal energy changes the state
- without changing the temperature
Question: In Figure 2, What change of state occurs between 200 seconds and 750 seconds?
liquid to gas
