When do you use q=mc(Tf-Ti) versus q=c(Tf-Ti) in thermochemistry calculations?

[genevievelily]

Hello,

I am currently studying intro to thermochemistry. I noticed in some problem solutions the equation q=mc(Tf-Ti) but in other the equation is q=c(Tf-Ti). How come sometimes the mass is not used in the equation? When do you know which one to use?

Thanks!

 

[Yanick]

In one case you are using the Heat Capacity which has units of J/K, in the other case they are using the Specific Heat Capacity which has units of J/(gK) or J/(molK). The latter is an intensive property of a system, meaning you don't have to worry about how much material you have, whereas the former can change depending on how much material you are working with. To intuitively understand this a little better just consider that 1g of water will have a much greater change in temperature when absorbing 1 J of energy whereas 1000g of water may hardly change temperature at all.

The relation between them is nC_s = C, where I will define n to be the relevant mass unit (either moles or grams), C_s = specific heat capacity, and C = heat capacity.

 

[Sunfire]

The second one is "per unit mass", where the "unit mass" has to be in units consistent with the rest of the equation.