# Thermal energy

#### Specific Heat Capacity c

The specific heat capacity is the amount of thermal energy (Q) needed to raise a mass (kg) by a temperature ΔT by the formula:

\$\$Q = mcΔT\$\$

Specific heat is a measure of how much thermal energy is needed to raise a mass's temperature. Each material has its own characteristics, so has a unique specific heat capacity.

The symbol for specific heat is 'c', and has the unit J kg-1 K-1

#### Thermal Energy Q

The amount of thermal energy required to raise the temperature of a mass m and specific heat capcity c, by a temperature ΔT is:

Q = mcΔT

this formula does assume that c will not change with temperature.

If the thermal energy causes the substance to change state, c may change as a result. e.g. The specific heats of:

• water is 4.186 J/g-K
• ice 2.108 J/g-K
• water vapour 1.996 J/g-K

#### Latent Heat

Latent heat is often used in the calculation of the thermal energy required to cause a change of state: latent heat of fusion (melting) and latent heat of vaporization (boiling).

The symbol of latent heat is L.

L = Q/m

The latent heat of fusion of copper is: Lf = 200 kJ kg-1

#### Example Questions

Question: how much energy would it take to melt 100g of ice which is currently at -10 °C?

Solution: ΔT = 10 K. This will bring the ice block to zero degrees celcius.

Q = mcΔT = (100g) . (4.186 J/g-K) . 10 K = 4186 J

Question: how much power is required to melt one tonne of copper?

Solution: The latent heat of fusion of copper is Lf = 200 kJ kg-1

Q = Lf.m = 200 kJ kg-1 . 1000 kg = 2.0 x 105 kJ = 200 MJ.

The power required is 200 MW-s, or 55 kWh.

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