When equal masses of the first (5°C) and third (39°C) liquids are mixed, the equilibrium temperature will be 22°C. This can be found using the equation avgT = (m1*T1 + m2*T2)/(m1+m2), where avgT is the average temperature, m1 and m2 are the masses of the first and second liquids respectively, and T1 and T2 are the temperatures of the first and second liquids respectively.
In the first scenario, we are mixing equal masses of the first (5°C) and second (19°C) liquids. Therefore, m1 = m2 = m, and T1 = 5°C and T2 = 19°C. Plugging this into the equation yields avgT = (m*5 + m*19)/(m+m), which simplifies to avgT = (5m + 19m)/2m = 24m/2m = 24/2 = 12°C. Since this is the equilibrium temperature, this means that it is also equal to the final temperature of the mixture, which is 13°C.
In the second scenario, we are mixing equal masses of the second (19°C) and third (39°C) liquids. Therefore, m1 = m2 = m, and T1 = 19°C and T2 = 39°C. Plugging this into the equation yields avgT = (m*19 + m*39)/(m+m), which simplifies to avgT = (19m + 39m)/2m = 58m/2m = 58/2 = 29°C. Since this is also the equilibrium temperature, this also means that it is equal to the final temperature of the mixture, which is 33.2°C.
Using the same equation and the values for the first and third liquids (5°C and 39°C), we can find the equilibrium temperature for when equal masses of the first and third are mixed. Plugging the values into the equation yields avgT = (m*5 + m*39)/(m+m), which simplifies to avgT = (5m + 39m)/2m = 44m/2m = 44/2 = 22°C. This is the equilibrium temperature when equal masses of the first and third liquids are mixed.