# Thermodynamics

#### 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.

## Site Index

### Latest Item on Science Library:

The most recent article is:

Air Resistance and Terminal Velocity

View this item in the topic:

Mechanics

and many more articles in the subject:

### Environment

Environmental Science is the most important of all sciences. As the world enters a phase of climate change, unprecedented biodiversity loss, pollution and human population growth, the management of our environment is vital for our futures. Learn about Environmental Science on ScienceLibrary.info.

### Great Scientists

#### Maurice Wilkins

1916 - 2004

Maurice Wilkins, 1916 - 2004, molecular biologist, was 'the third man of the double helix', as his biography title declares. Born in New Zealand, but did most of his professional work in England, Wilkins shared the Nobel Prize with Crick and Watson.