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 $m \,g/s$. 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 $800 \,cal)$

• 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.
$(Mg) (1 \,cal/m^{\circ}C) (80 - 60^{\circ}C) = 80 \,cal$
or, $M = 40 \,g$
$\therefore m = 4 \,g$