Specific Heat Capacity

Heat energy

All these facts are related to heat energy and to a quantity known as specific heat capacity and we can explain them by looking more closely at heat energy.

Over the past few centuries scientists have putforward some very strange theories about the nature of heat. One of these was that heat was some sort of a fluid that you added to a body to make it hot and took away from a body to cool it down.

However, during the last century two men, Rumford and Joule, both proposed the idea that heat was related to energy. When heat energy passes into a body it increases the internal energy of the body. Rumford demonstrated this in some well-known experiments in cannon boring and Joule showed that the friction generated between a paddle wheel and some water would heat up the water.

We can summarise these results as:

Heat capacity and specific heat capacity

The amount of heat energy needed to change the temperature of a substance depends on:

(a) what the substance is;

(b) how much of it is being heated;

The heat energy needed to raise the temperature of an object by 1 K is called the HEAT CAPACITY of the object.

However, a rather more useful quantity is the heat energy needed for 1 kg only.

Specific heat capacity is given the symbol c. The units for c are J/(kg K) or J/(kgoC).

The values for the specific heat capacities of some common substances are given in the following table:

Substance / Specific heat capacity (J/(kgK) / Substance / Specific heat capacity (J/(kgK)
Water / 4200 / Aluminium / 913
Cast iron / 500 / Brick / 2300
Copper / 385 / Concrete / 3350
Lead / 126 / Marble / 880

Remember that substances with high specific heat capacities take a lot of heat energy and therefore a long time to heat up and also a long time to cool down.

One interesting effect is the way in which the land heats up quicker than the sea - the specific heat capacity of sea water is greater than that of the land and so more heat energy is needed to heat it up by the same amount as the land and so it takes longer. It also takes longer to cool down.

The heat energy needed to raise the temperature of m kg of a substance of specific heat capacity cby  K is given by the equation:

If the object cools then it gives out heat energy and if it heats up it takes in heat energy.

Conversion of mechanical energy to heat

When an object falls to the ground, the potential energy that it had at the top is converted to kinetic energy that finally becomes heat energy.

Assuming no loss of energy to any other forms we can work out the rise in temperature of water falling over a high waterfall.

There must be no residual kinetic energy of spray and no sound must be made! (Clearly not true but it is the best we can do without making the problem very difficult).

This conversion of gravitational potential energy into heat energy can be used in the laboratory to measure the specific heat capacity of lead shot.