Question

Figure shows three containers. The rightmost container contains water (heat capacity $5cal{/}^{\circ }C$), initially at temperature ${100}^{\circ }\text{C}$. The middle container contains water maintained at ${80}^{\circ }\text{C}$ with the help of a heater. The container at the left hand side contains ice at $0^{\circ }\text{C}$. There are two heat conducting rods $A$ and $B$ both having thermal resistance equal to ${10}^{\circ }\text{C}\text{s/cal}$. Disregard any heat loss in the surrounding.


Find the rate with which ice melts in the leftmost container.

• A. $0.1\text{g/sec}$
• B. $1\text{g/sec}$
• C. $10\text{g/sec}$
• D. $8\text{g/sec}$

Answer 1

The correct option is A $0.1\text{g/sec}$


Thermal current throught A $i_3=\frac{\Delta T_A}{R_A}=\frac{80-0}{10}=8cal/s=\frac{dQ}{dt}$

For melting of ice,

$dQ=dm{L}_f$

$\Rightarrow \frac{dQ}{dt}=\frac{dm}{dt}{L}_f$

$\Rightarrow 8cal/s=\frac{dm}{dt}\times 80cal/g$

$\Rightarrow \frac{dm}{dt}=0.1g/s$