Question

What will be the new temperature of water ,if $50g$ of water at a temperature of ${30}^{\circ }C$ is added to $200g$ of water at a temperature of ${100}^{\circ }C$?

• A. ${68}^{\circ }C$
• B. ${80}^{\circ }C$
• C. ${74}^{\circ }C$
• D. ${86}^{\circ }C$
• E. ${92}^{\circ }C$

Answer 1

Answer: (D)

${86}^{\circ }C$

$200$ g water at ${100}^{o}C$ release some heat which is completely absorbed by $50$ g water at ${30}^{o}C$ such that the net heat exchanged between system and surrounding is zero.
Let the new temperature of the water be $T$ ${}^{o}C$ and heat capacity of water be $S$.

$\therefore$ $50\times S\times (T-30)+200\times S\times (T-100)=0$

OR $T-30+4(T-100)=0$

OR $5T=430$ $⟹T={86}^{o}C$