Question

When an unknown amount of water at ${70}^{\circ }C$ is added to $175g$ of water at ${30}^{\circ }C$, the equilibrium temperature becomes ${42}^{\circ }C$. Find the mass of water added.

• A. $10g$
• B. $25g$
• C. $75g$
• D. $100g$

Answer 1

Answer: (C)

$75g$

Let $m$ be the mass of water added .

Heat given by hot water at ${70}^{o}C$ $=mc(70-42)$

Heat taken by cold water at ${30}^{o}C$ $=175c(42-30)$

By the principle of mixtures ,

$mc(70-42)=175c(42-30)$

or $m\times 28=175\times 12$

or $m=75g$