Question

Heat is being supplied at a constant rate to a sphere of ice which is melting at the rate of 0.1 gm /sec. It melts completely in 100 sec. The rate of rise of temperature thereafter will be

• A. ${0.8}^{0}C/sec$
• B. ${5.4}^{0}C/sec$
• C. ${3.6}^{0}C/sec$
• D. will change with time

Answer 1

The correct option is A ${0.8}^{0}C/sec$

Rate of melting of ice is $0.1gmse{c}^{-1}$

Total mass of ice $m_{ice}=0.1\times 100=10gms$ since all the ice melts in $100$ secs.

Total amount of heat supplied to melt $10$ gms of ice $Q=10\times 80cal=800cal$

Rate at which heat is supplied $\frac{dQ}{dt}=\frac{800}{100}=8calse{c}^{-1}$

After all the ice melts, the water temp will rise.

Rate of rise of temp of water $\frac{dT}{dt}=\frac{\frac{dQ}{dt}}{m_{water}\times s_{water}}=\frac{8}{10\times 1}={0.8}^{0}Cse{c}^{-1}$