Question

The temperature of equal masses of three different liquids $A,B,C$ are ${12}^{o}C,{19}^{o}C$ and ${28}^{o}C$ respectively. The temperature, when $A$ and $B$ are mixed, is ${16}^{o}C$ and when $B$ and $C$ are mixed, is ${23}^{o}C$. What will be the temperature when $A$ and $C$ are mixed?

Answer 1

Let a, b and c be the specific heat capacities of liquids A, B and C

Let the mass of the liquids be m, when A and B are mixed.

ma($16-12$)=mb($19-16$)

$\Rightarrow 4a=3b$

When B and C are mixed.

mb($23-19$)=mc($28-23$)

$\Rightarrow 4b=5c$

Therefore $16a=12b=15c$

Let $x$ be the temperature when A and C are mixed.

ma($x-12$)=mc($28-x$)

$\Rightarrow \frac{a}{c}=\frac{15}{16}=\frac{28-x}{x-12}\Rightarrow 15x-180=448-16x\Rightarrow 31x=628\Rightarrow x=20.25degree$