## 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

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

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

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

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.

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.

• 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

liquid to gas