# Latent Heat and Phase Change

When an object changes from gas to liquid or liquid to solid, or back, we call it a change of phase. The heat required to change 1kg of a substance from solid to liquid is the Heat of Fusion. The heat required to change 1kg of a substance from liquid to gas is the Heat of Vaporization. Both of these are called Latent Heats. The heats of Fusion and Vaporization are also the same when the process is going back the other way (i.e. changing from a gas to a liquid and changing from a liquid to a solid.) We'll treat the problem the same way.

When we heat a substance up, there are two regions or situations that we look at. The first is the area where we are keeping the substance in the same phase and just changing the temperature. Here, the Heat added (Q) equals the mass times the specific heat of the substance times the change in temperature, or

Q = mcDT.

This works whether we are heating the substance up (adding heat) or cooling the substance down (subtracting heat).  The second type of transformation that takes place is a phase change. When we perform a phase change, the substance remains at the same temperature throughout the phase change. The heat added (or subtracted) depends upon the Latent Heat and the mass of the substance. This is kind of an interesting phenomenon. When you boil a pot of water on the stove, for example, turning the heat up once the water is boiling does not increase the temperature of the water. It only causes the water to evaporate faster. Turning the heat down until the water is just boiling will cook your food as quickly, and save energy. Anyway, the heat added or subtracted is given by the formula

Q = mL

where m is the mass and L is the Latent Heat of Vaporization or Fusion, depending on your case. Probably the easiest way to illustrate this is to follow the process of raising a block of ice from -40oC to 120oC steam. The graph below gives us temperature vs heat for the process. Let's look at each region.

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The Latent Heat of Fusion (Lf) for water is 3.33 x 105 J/Kg.  The Latent Heat of Vaporization (Lv) for water is 22.6 x 105 J/kg. Notice that it takes a lot more energy to turn water into steam than it does to melt ice. This makes sense - steam as a gas has a lot more kinetic energy per molecule than water - that is one reason it is so dangerous.

The specific heat for water is 4186 J/kg oC. The specific heat for ice is 2100 J/kg oC and the specific heat for steam (water vapor) is 2010 J/kg oC. So how much heat is required to raise a 1 kg block of ice from -40 oC to 120 oC? Let's do this by section.

• To raise the temperature of ice from - 40 oC to 0oC: Q =mcDT = (1 kg)(2100 J/kg oC)(40oC) = 84000 J.
• To melt the ice at 0oC: Q = mLf = (1 kg)(3.33 x 105J/Kg) = 3.33 x 105 J.
• To raise the temperature of the water from 0 oC to 100oC: Q= mcDT = (1 kg)(4186 J/kg oC)(100oC) = 418600 J.
• To turn the water to vapor at 100oC: Q = mLv = (1 kg)(22.6 x105 J/kg) = 22.6 x 105 J.
• Toraise the temperature of the steam from 100 oC to 120oC: Q = mcDT = (1 kg)(2010 J/kg oC)(20oC) = 40200 J.

The total heat required is the sum of all of the above heats, or 3.14 x 106 Joules (rounding and applying significant digits.)