Question

A $100\text{cm}$ long cylindrical flask with inner and outer radius $r_1=2\text{cm}$ and $r_2=4\text{cm}$ respectively, is completely filled with ice at $0^{\circ }C$ as shown in the figure. The constant temperature outside (surrounding) the flask is ${40}^{\circ }C$. Assume heat exchange occurs only through the curved surface of the flask. Thermal conductivity of the flask is $0.693{\text{W/m}}^{\circ }C,L_{ice}=80\text{cal/gm}$ and $1\text{cal}=4200J$

• A. Rate of heat flow from surrounding to the flask is $80\pi J/s$.
• B. The rate at which ice melts is $\frac{\pi }{4200}\text{Kg/s}$.
• C. The rate at which ice melts is $100\pi \text{Kg/s}$.
• D. Rate of heat flow from surrounding to the flask is $40\pi J/s$

Answer 1

Answer: (A), (B)

The rate at which ice melts is $\frac{\pi }{4200}\text{Kg/s}$.

$H=\frac{KAd\theta }{dr}=K\left(2\pi rL\right)\frac{d\theta }{dr}$
$\therefore H{\int }_2^4\frac{dr}{r}=2\pi KL({\theta }_2-{\theta }_1)=80\pi$
$\Rightarrow \frac{dm}{dt}L=80\pi$
$\Rightarrow \frac{dm}{dt}=\frac{80\pi }{L}=\frac{80\pi }{80\times 4200}=\frac{\pi }{4200}\text{Kg/second}.$