# Latent Heat of Water

In talking about the heats involved in changing temperatures, one thing we’ve neglected is what happens when a material changes phase. We talked about the three phases – gas, liquid and water. When a material changes from one phase to another, we call this a phase transition or change of phase.
Changes from the solid to the liquid or from the liquid to the gaseous state, and vice versa, are called phase changes. They always
involve a transfer of heat, even though the temperature of the substance undergoing the phase change stays constant. The heat flow from one object to another can change either the average
kinetic energy of the random motion of the molecules, which changes the temperature of the object, or can change the average potential energy of the molecules, which causes the phase of the object to change. Consider what happens when, for instance, a pot of water is heated on a stove.
At first, the temperature rises. Upon reaching 100 o C (212 o F) the temperature stops increasing, even though the flame keeps supplying heat at the same rate as before. We know that the

target=”_blank”>thermal energy

supplied goes into breaking the bonds between the molecules, while the kinetic energy of the molecules remains unchanged. Gradually, more and more molecules gain sufficient energy to overcome the inter molecular forces binding the molecules one to the other. A similar phenomenon occurs when ice melts.

We call the heat required to produce a phase change the latent heat (L’Heat). Two examples of latent heat are the heat of freezing and the heat of vaporization. The heat of freezing is the amount of thermal energy given off as a liquid freezes, and the heat of vaporization is the amount of thermal energy that must be added to change a liquid to a gas.

Heat added or subtracted for a phase change = Latent heat x Mass

Q = L heat M
Where Q = heat (calories or joules) L heat = latent heat (calories/gram or joules/gram) M = mass (grams)

If liquid water at 100 o C is changed into steam, the heat added (the latent heat of vaporization) is 540 calories for every gram of water. If steam at 100 o C is changed into water at 100 o C, 540 calories for every gram of steam must be subtracted. If ice at 0 o C is changed into liquid water at 0 o C, the heat added (the latent heat of melting) is 80 calories for every gram of ice. If liquid water at 0 o C is change into ice at 0 o C, 80 calories for every gram of liquid water must be subtracted.

Latent heats can be very large. For example, the latent heat of vaporization of water is 540 cal/g and the latent heat of freezing of water is 80 cal/g. Therefore, changing a given quantity of water to steam requires 5.4 times as much heat as warming it from 0 o C (+32 o F) to 100 o C (212 o F), and melting ice requires as much heat as warming water from 20 o C (68 o F) to 100 o C.

#### Practise This Question

When a magnet is moved quickly towards a closed coil the induced emf and charge are e' and q'.  When the same magnet is slowly towards the same coil, the induced emf and charge are e1 and q1  respectively.  Then