Question

Which of the following would raise the temperature of $20\text{g}$ of water at ${30}^{o}C$ most, when added to water ?
(Specific heat of copper is $0.1{\text{cal.g}}^{-1}{C}^{-1}$)

• A. $20\text{g}$ of water at ${40}^{o}C$
• B. $20\text{g}$ of water at ${27}^{o}C$
• C. $1\text{kg}$ of coper at ${25}^{o}C$
• D. $4\text{g}$ of water at ${80}^{o}C$

Answer 1

The correct option is D $4\text{g}$ of water at ${80}^{o}C$

Only a substance at higher temperature will be able to raise temperature of water at ${30}^{o}C$ so, option (B) and (C) are rejected.
A) When $20\text{g}$ of water at 40${}^{o}C$ is added then, from principle of calorimetry
Heat lost =Heat gained
$20\times 1\times (40-T)=20\times 1\times (T-30)$
$800+600=40T\Rightarrow T=\frac{1400}{40}={35}^{0}C$
So, this raise temperature by 5${}^{o}C$

D) when $4\text{g}$ added water at ${80}^{o}C$ is added then
heat lost =heat gained
$4\times 1\times (80-T)=20\times 1\times (T-30)$
$920=24T\Rightarrow T={38.3}^{0}C$
So, this raise the temprature by ${8.3}^{o}C$