Question

Which one of the following would raise the temperature of $20\text{g}$ of water at ${30}^{\circ }\text{C}$ most when mixed with ?
(Specific heat of water $=1{\text{cal/g}}^{\circ }\text{C}$)

• A. $20\text{g}$ of water at ${40}^{\circ }\text{C}$
• B. $40\text{g}$ of water at ${35}^{\circ }\text{C}$
• C. $10\text{g}$ of water at ${50}^{\circ }\text{C}$
• D. $10\text{g}$ of water at ${80}^{\circ }\text{C}$

Answer 1

The correct option is D $10\text{g}$ of water at ${80}^{\circ }\text{C}$

Let $m\text{g}$ of water whose temperature is ${\theta }_0(>{30}^{\circ }\text{C})$ and specific heat is $1{\text{cal/g}}^{\circ }\text{C}$ be added to $20\text{g}$ of water at ${30}^{\circ }\text{C}$ and let $\theta$ be the final temperature of the mixture.
So,
$m\left(1\right)({\theta }_0-\theta )=\left(20\right)\left(1\right)(\theta -20)$
$\therefore \theta =\frac{400+m{\theta }_0}{20+m}$
The right hand side is maximum for option (d). Therefore, the correct answer is (d).