Calorimetry

The quantitative equation relating heat and changes in temperature is given as:

Where the change in heat is given as Q(measured in joules), m is the mass of the substance, the change in temperature of the substance is self-explanatory, and C is a quantity known as the specific heat capacity.


The specific heat capacity of a substance is defined as the amount of heat required to increase the temperature of a substance by 1 unit(it could be Kelvins, Celsius, Fahrenheit, etc. depending on the units of the specific heat capacity), given that the substance has a mass of 1 unit(could be any unit of mass as long as that unit is in the units of the specific heat capacity).


Specific heat capacity is usually measured in Joules/(Kilogram Celsius) or Joules/(Kilogram Kelvin).


It's quite difficult to predict the specific heat capacity of a substance as most of them are experimentally found. A table of specific heat capacities is provided below:

Now, imagine an isolated system where all you have is a metal cube and a cup of water, both at different temperatures. If you drop the metal into the water, there will be heat transfer between the two. However, keep in mind that the energy of the system is the same because it's isolated. So, what does this mean?


Well, let's say the metal cube is at about 83 degrees Celsius and the water is at 2 degrees Celsius. The heat will transfer from the metal to the water since the metal is hotter. Since the total energy of the system is conserved, this means that the heat gained by the water is equal to the heat lost by the metal, mathematically equivalent to:


Note: These two temperatures given are arbitrary and can be any two values so long as the metal's temperature is greater than the water's.



Note: These two temperatures given are arbitrary and can be any two values so long as the metal's temperature is greater than the water's.


If heat is transferred to a system through the surroundings, then the heat transfer process requires heat, so it's endothermic. In contrast, if a process causes the solution/mixture to have a temperature increase, the process is exothermic.

Latent Heat

When substances undergo phase changes(at their melting and boiling points), their temperatures don't change. Instead, the energy being added or taken away is to initiate the actual change of phase for the substance instead of warming or cooling it. This can be seen in the diagram below for water:

When the water isn't undergoing a phase change, the temperature changes. If it is changing phase, the temperature stays constant and the width of the flat line at the phase change represents how much energy is necessary to make that phase change happen.


The heat required to entirely cause it to change phase from solid to liquid(or vice versa) is called the latent heat of fusion, denoted as Lf°. Note that the heat of fusion is negative if you freeze a substance, and the heat of fusion is positive if you melt a substance.


The heat required to entirely cause it to change phase from liquid to gas(or vice versa) is called the latent heat of vaporization, denoted as Lv°. Note that the heat of vaporization is negative if you condensate a substance, and the heat of vaporization is positive if you vaporize a substance.


The total heat brought on by a phase change is:

If you're heating a substance and it goes through a phase change but also just changes temperature, you treat both heating processes differently. One term goes for every line segment on the graph above. Each sloped line has its own heat term. You can't treat warming/cooling a substance the same at any phase because different phases of substances often have different specific heat capacities. Similarly, each flat line for phase changes has its own heat term. Thus, if we took a cube at -20 C like in the graph above and we heat it to 120 C, the total heat in the process is given by:

We get the temperature heating of the ice, the phase change energy of the ice to water, the temperature heating of the water, the phase change energy of the water to vapor, and the temperature heating of the vapor.


The latent heats of vaporization and fusion, along with melting and boiling points, for various substances are shown below:

Citations/Attributions