Question

Three liquids are at temperatures of 13◦C, 19◦C, and 31◦C, respectively. Equal masses of the first two liquids are mixed, and the equi- librium temperature is 16◦C. Equal masses of the second and third are then mixed, and the equilibrium temperature is 24.3◦C.

Find the equilibrium temperature when equal masses of the first and third are mixed.

Answer in units of ◦C.

Answer 1

$16=\frac{13+19}{2}\implies c_1=c_2,$

$24.3=\frac{19c_1+31c_3}{c_1+c_3}\implies$

$5.3c_1=6.7c_3\implies c_3=0.791c_1,$

$t=\frac{13c_1+31c_3}{c_1+c_3}=\frac{13+31\cdot 0.791}{1.791}=21°C.$