Science Library - free educational site

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.

Content © Andrew Bone. All rights reserved. Created : December 18, 2013 Last updated :February 14, 2016

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:

Subject of the Week

Mathematics

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.

Mathematics

Great Scientists

Maurice Strong

1929 - 2015

Maurice Strong was a man of extraordinary achievement and a dedicated environmentalist, despite his early life's achievement of rags-to-riches, making his fortune from the oil industry.

Maurice Strong, 1929 - 2015, environmentalist and policy-maker
ScienceLibrary.info

Quote of the day...

"I knew Descartes," said Isaac Barrow. "René', I used to say. 'Have you got des cartes?' Then after a few tankards, he would say: 'Don't try to cheat me, Wheelie-boy. Cogito ergo sum...' - that's classical pidgin for 'I can think so I can add up as well as the next man'."

ZumGuy Internet Promotions

Renewable energy media services