Heat Capacity and Latent Heat

All matter is made up of molecules that vibrate at different speeds. The temperature of an object is as a result of it's internal kinetic energy. If sufficient energy is transferred to the object, the speed at which the molecules vibrate would increase and it would be noted by a rise in temperature.

The heat capacity, C is the amount of heat that is required to raise the temperature of a mass by 1 degree Celsius.

Specific Heat Capacity, c is the amount of heat that is required to raise the temperature of a mass of 1 kg by 1 degree Celsius. It is measured in J kg-1 0C-1 .

The amount of heat transferred to an object can be calculated using the formula - heat energy = mass x specific heat capacity x change in temperature

Heat capacity, C and specific heat capacity, c are related to in the following equation

c = C/m

c water = 4200 J kg-1 0C-1. This means that it would take 4200J of energy to change the temperature of 1 kg of water by 1 degree celsius.

csilver = 240 J kg-1 0C-1

Calculate the amount of heat required to:

i) change 5 kg of silver by 4 0C

ii) raise the temperature of 200 g of water from 40 K to 53 K.

Latent Heat

is referred to as hidden heat.

This is the heat that is required to change the state of a substance without a change in temperature. It occurs at the melting point or the boiling point and depends on the mass and the specific latent heat of the substance. The resulting equation is E = ml.

It is measured J kg-1

The specific latent heat of vapourization (lv) of a substance is the quantity of heat required to change a unit mass of liquid to a gas without a change in temperature. This occurs at the boiling point.

lv water = 2 260 000 J kg-1

The specific latent heat of fusion of a substance lf is the quantity of heat required to change a unit mass of a solid to a liquid without a change in the temperature. This occurs at the melting point.

lf ice = 334 000 J kg-1

This means that it takes 334 000 J of energy to change 1 kg of ice to 1 kg of liquid.

Question

Why is the latent heat of vaporization of water greater than the latent heat of fusion of water?

Answer: The latent heat of fusion and vaporization both involve the heat required to change the state of a substance without a change in temperature. In the case of the latent heat of fusion it is the heat required to change a substance from a solid (ice) to a liquid (water) or vice versa while the latent heat of vaporization from a liquid (water) to a gas (steam) or vice versa.

In solids, the molecules are very close together and the attraction between the molecules are great. This causes a substance to have a structure in which the molecules have little freedom to move, as you would see in the case of ice. In the case of a liquid, the molecules are closely spaced, though not as closely spaced as a solid, they have more freedom to move and the intermolecular forces are weaker that that of a solid. Thus a liquid can flow, unlike a solid. Now in a gas, the molecules are sufficiently far apart that there are little to no attractive forces. Because of this a gas can easily be compressed and take the shape of the container.

Now as you heat a solid turning it into a liquid, you increase the kinetic energy of its molecules, moving them further apart until the forces of attraction are reduced to allow it to flow freely. Keep in mind the forces of attraction still exists. Now as you heat a liquid, turning it into a gas, the kinetic energy of the molecules are increased to a point where there are no forces of attraction between the molecules.

The energy required to completely separate the molecules, moving from liquid to gas, is much greater that if you were just to reduce their separation, solid to liquid. Hence the reason why the latent heat of vaporization is greater that the latent heat of fusion.