Question

One litre of water at ${30}^{o}C$ is mixed with one litre of water at ${50}^{o}C$. The temperature of the mixture will be

• A. 80C
• B. more than 50C but less than 80C
• C. 20C
• D. between 30C and 50C

Answer 1

The correct option is D between 30C and 50C

Let the first volume of water be V1. Let the second volume of water be V2. Let the initial temperature of the first volume of water be θ1. Let the initial temperature of the second volume of water be θ2.

Let the energy required to heat a unit volume of water by unit temperature by C.

So, if the final temperature is θfinal, we have

heat gained by the first volume of water

$=V_1\times C\times ({\theta }_{final}-{\theta }_1)$

and

heat lost by the second volume of water

$=V_2\times C\times ({\theta }_2-{\theta }_{final}).$

By the law of conservation of energy,

heat lost = heat gained

∴$V_1\times C\times ({\theta }_{final}-{\theta }_1)=V_2\times C\times ({\theta }_2-{\theta }_{final})$

∴$V_1{\theta }_{final}-V_1{\theta }_1=V_2{\theta }_2-V_2{\theta }_{final}$

∴${\theta }_{final}=V_1{\theta }_1+V_2{\theta }_2{V}_1+V_2$

Substituting the given values,

${\theta }_{final}=\frac{30+50}{2}={40}^{\circ }C$.

The answer is option D