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}

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 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: L_{f} = 200 kJ kg^{-1}

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 L_{f} = 200 kJ kg^{-1}

Q = L_{f}.m = 200 kJ kg^{-1} . 1000 kg = 2.0 x 10^{5} kJ = 200 MJ.

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

Content © Andrew Bone. All rights reserved. Created : August 31, 2014

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Mathematics is the most important tool of science. The quest to understand the world and the universe using mathematics is as old as civilisation, and has led to the science and technology of today. Learn about the techniques and history of mathematics on ScienceLibrary.info.

1879 - 1968

Otto Hahn, 1879 - 1968, was a German chemist, who was awarded the Nobel Prize for Chemistry in 1944 for his discovery of fission.

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