First slide

Heat transfer

Question

Ice starts forming on the surface of the lake and takes 8 hrs to form a layer of 11 cm thick. How much time will it take to increase the thickness of layer by 2 cm further?

Moderate

A

8 hours
B

less than 3 hours
C

between 8 to 16 hours
D

3.17 hour

Solution

$t i m e r e q u i r e d t o f o r m x t h i c k n e s s o f i c e i s t= \frac{ρL}{2Kθ} {(x}_{2}^{2} - {x_{1}}^{2}) here ρ is density of ice; L is latent heat of fusion of ice; K i s c o e f f i c i e n t o f t h e r m a l c o n d u c t i v i t y; θ i s t e m p e r a t u r e o f a t m o s p h e r e t α {(x}_{2}^{2} - {x_{1}}^{2}) t_{1} {=8 hours; x}_{1} =0cm; x_{2} =0 cm; x_{3} = 13 cm t_{2} =? \frac{t_{1}}{t_{2}} = \frac{{(x}_{2}^{2} - {x_{1}}^{2})}{{(x}_{3}^{2} - {x_{2}}^{2})} \frac{8}{t_{2}} = \frac{11^{2} - 0^{2}}{13^{2} - 11^{2}} t_{2} = \frac{8 x 48}{121} =3.17 hour$

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