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.


The temperature of water in the rightmost container decreases with time. The rate with which the ice melts in the leftmost container

• A. will decrease with time
• B. will increase with time
• C. will remain steady
• D. will increase and then decrease

Answer 1

The correct option is C will remain steady


The thermal current flowing into the ice container is
$i_3=\frac{\Delta T_A}{R_A}=\frac{80-0}{10}=8cal/s=\frac{dQ}{dt}$

Therefore $\frac{dQ}{dt}=\frac{dm}{dt}{l}_f=8cal/s$

Rate at which ice melts will remain constant.