Let's say that I have two, different fluids that are miscible and are of two different temperatures. How can I calculate the temperature of a mixture of the two fluids? Without a thermometer, of course.
First of all you have to have the Mass, Heat capacity and the Temperature of each fluid. then you can calculate the final temperature.
$Q = M.C.Delta(T)$
where $M$ is the mass, $C$ is heat capacity and $Delta(T)$ is the amount of changes in the temperature. first calculate how much energy do they take to get to the 0 temperature. let me show you in an example:
Imagine I have 2 kilograms of fluid 1 with heat capacity of 1.5 and with 25 degrees in Celsius. and 5 kilograms of fluid 2 with capacity of 0.5 and temperature of 40 degrees. I imagine they get to the 0 degrees of Celsius and then calculate how much energy they produce.
$Q1 = 2*1.5*25 = 75 J$
$Q2 = 5*0.5*40 = 100 J$
So I have total amount of 175 joules and two fluids. now this heat (energy) is divided to these two fluids. where first fluid gets E1 and the second one gets E2 amount of Energy. and I know that:
$E1+E2 = 175 J (1)$
Now If I use my main equation to determine the temperature that they rise to, I can get an answer. remember that both fluids get to a certain temperature that I call FT (Final Temperature) :
$E1 = 2*1.5*FT = 3*FT$
$E2 = 5*0.5*FT = 2.5*FT$
If I sum the two equation and use my equation (1), I can calculate the final temperature. see:
$E1 + E2 = 3*FT + 2.5*FT$
$175 = FT (3 + 2.5) = 5.5 * FT$
So : $FT = 175/5.5 = 31.81$ Degrees of Celsius
So that final temperature of the two fluids is about 31.81 . you can use other method too, but I used this method (turning them to 0 degrees of Celsius) to remove the delta from the formula.