# In order to solve for this equation for heat capacity, do I need to treat it as a system of equations?

For a lab, we took the temperature of 15ml of tap water, $q_{cool}$, then added 20ml of tap water warmed to 80 degrees Celsius, $q_{warm}$.

We recorded a baseline temperature of 24.8, a temperature of 56 after adding the water, and a temperature of 42.9 100 seconds later.

I have the following equations:

1. $q=m × 4.184 J/(g*C) × ΔT$
2. $q_{warm} + q_{cool} + q_{calorimeter} = 0$
3. $q_{calorimeter} = - (q_{warm} + q_{cool} ) = C_{calorimeter} × ΔT$.

In the first formula $4.184 J/(g*C)$ is the specific heat of water.

To the best of my knowledge, specific heat is usually expressed in grams-Kelvin; however, the TA may have provided the info in grams-Celsius (their units are equal, so I presume they're the same thing). However, she also uses $C$ to designate heat capacity as she does in the third equation.

If, in the first equation, $C$ designates heat capacity, then I have three equations, and three unknowns: $q_{calorimeter}, q_{warm}$, and $q_{cool}$, and I'd treat it as a system of three equations and solve for them.

However, if, in the first equation, $C$ designates 'Celsius' then I could just plug in the values for $q_{warm}$ and $q_{cool}$ and solve for $q_{calorimeter}$.

Two related questions:

1. In the first equation, what does $C$ designate.
2. If it designates the heat capacity of the system, do I solve for $q$ by solving a system of equations?

• In the wide world of science, sadly we don't have enough letters in any alphabet for what we need them to represent. One guideline that is helpful at least when typesetting: use emphasis/italics for quantities, constants, and variables (things that represent a number) - $C_{\text{p}}$. Use normal text for units $^\circ\text{C}$. – Ben Norris May 16 '15 at 12:27