# Latent heat

2009-08-04

This blog’s focus on matters of energy and climate frequently leads to discussions of thermodynamics. One aspect of that not yet mentioned is latent heat: the energy involved in phase changes of matter. While it takes 1 calorie (not one kilocalorie, as what people call food ‘calories’ are) to heat 1 ml (1 gram, 1 cubic centimetre – don’t you love metric) one degree Celsius, it takes a lot of energy to change that 1 mL of 100˚C water into 101˚C water vapour. Indeed, it takes 540 calories to induce the phase change (turning 1 g of ice into 1 g of water takes 80 calories).

An entertaining way to see this demonstrated is to watch Julius Sumner Miller (mentioned before) talk about temperature. Another is to watch an episode of James Burke’s The Day the Universe Changed: Credit Where It’s Due. As a bonus, it explains how religious dissenters helped to kick off the coal-fired Industrial Revolution in England, eventually generating the climate change problems that confront us so dauntingly now. There is also a fair bit of talk about banking, and the role it played in industrial development.

Matt August 4, 2009 at 3:52 pm

Indeed, latent heat is a very useful thing to understand. It is the reason sweat is cooling, that it takes longer for a pot to boil dry than it does to boil, etc.

Milan August 5, 2009 at 8:06 am

Does it take as much energy to evaporate one gram of non-boiling water as to convert one gram of hundred degree water to water vapour?

Matt August 5, 2009 at 1:06 pm

Well, it’s not the same and I can’t find the equation to see if it’s more or less. Basically, there are polynomial equations for latent heat where you can plug in the temperature and it spits out a value. The answers over small temperature ranges never vary greatly, and so my feeling is that the latent heat of vaporization at, say, body temperature is slightly more than at 100ºC.

It can be helpful to view enthalpy (heat due to temperature) as kinetic energy, and latent heat as potential energy that you get back when the water (or whatever) re-condenses.

. November 3, 2010 at 11:36 am

Example 2: melting ice. The latent heat of melting of ice is 6 kJ/mol, or 333 kJ per kg, a quantity I have never been able to memorise… until now! Using the same trick as above, we can convert this into an equivalent temperature rise, by dividing by the heat capacity. The answer is “the latent heat of melting of ice ‘is’ 80 degrees C”.
I don’t think I’ll forget that number! It really brings home why mountaineers spend so much time melting snow. The energy to melt the snow is roughly the same as the energy to bring the melted snow up to boiling point!

Example 3: vaporizing water. We can apply the same trick to the heat required to vaporize water (2258 kJ/kg). The answer is (2258 kJ/kg) / (4.2 kJ/kg/C) in C = 538 C. This number violates the “should be between 1 and 200” rule, so it is not super-memorable, but it is quite striking, isn’t it – whereas near-boiling water is 373 degrees above absolute zero, the energy required to actually boil it is equivalent to another 538 degrees of temperature rise! Maybe the best way to obey the “1-200” rule is to reexpress this heat once more, comparing it to the energy required to bring the water from 0 to 100 C. It is bigger by a factor of 5.4. So “the time for the kettle to boil itself dry is about 5 times the time taken to bring it to the boil”.
Here ends the lesson.