Question

Heat is being supplied at a constant rate to a sphere of ice which is melting at the rate of $0.1\text{gm/sec}$. It melts completely in $100\text{sec}$. The rate of rise of temperature thereafter will be (Assume no loss of heat)

• A. $0.8{}^{\circ }\text{C/sec}$
• B. $5.4{}^{\circ }\text{C/sec}$
• C. $3.6{}^{\circ }\text{C/sec}$
• D. Will change with time

Answer 1

The correct option is A $0.8{}^{\circ }\text{C/sec}$

Required heat to melt $0.1$ grams of ice per second is $\Delta Q/\Delta t=0.1\times 80=8\text{cal/s}$
Amount of ice converted to water is $=0.1\times 100=10\text{gm}$

Rate of rise in temperature will be $\frac{\Delta T}{\Delta t}=\frac{\Delta Q/\Delta t}{ms}=8/(10\times 1)={0.8}^{\circ }\text{C/s}$.