Question

A vessel contains $M$ grams of water at a certain temperature and water at certain other temperature is passed into it at a constant rate of $mg/s$. The variation of temperature of the mixture with time is shown in figure. The values of $M$ and $m$ are, respectively (the heat exchanged after a long time is $800cal)$

• A. $40$ and $2$
• B. $40$ and $4$
• C. $20$ and $4$
• D. $20$ and $2$

Answer 1

Answer: (B)

Evidently the initial temperature of the water contained in the vessel $(Mg)$ is $80^{\circ }C$, and the temperature of the water passed into it is $60^{\circ }C$, as the final temperature of the mixture tends to attain a value of $60^{\circ }C$.
$M\times 1(80-70)=m\times 10\times 1(70-60)$
or, $M/m=10$
Since the heat exchanged after a long time is $800$ cal.
$(Mg)(1cal/m^{\circ }C)(80-60^{\circ }C)=80cal$
or, $M=40g$
$\therefore m=4g$