Growth of Ice on Lake
Growth of Ice on Lake :- The growth of ice on a lake is a fascinating natural process that occurs during cold weather conditions. When the air temperature drops below freezing (0°C or 32°F), the heat from the lake’s surface is transferred to the colder air, causing the water at the surface to lose heat and freeze.
Consider a lake of surface area A. Let at any time t thickness of ice on the surface of the lake = y and air temperature = –θ° C. The temperature of water in contact with the lower surface of ice = 0°C
Rate of heat loss from the surface of lake to atmosphere, through ice slab of thickness y is given by :-
This dQ is the heat loss of extra thickness(dx) of ice.
Mass of this extra thickness of ice, dm = ρiceV = ρice A dy
From equations (1) and (2),
So time taken by ice to grow a thickness y is
(1). Time taken by ice to grow from thickness y1 to thickness y2 is
(2). If at t = 0, y = 0, then the ratio of time taken to double and triple the thickness :
Ice starts forming in a lake with water at 0°C when the atmospheric temperature is -10°C. If the time taken for the first 1 cm of ice to be formed is 7 hours, then the time taken for the thickness of ice to change from 1 cm to 2 cm is:
(A) 7 hours
(B) 14 hours
(C) 21 hours
(D) 3.5 hours
If time taken for the formation of 1 cm of ice(thickness) on a lake is 4 minutes, then calculate time taken in the formation of 4th cm of ice.
In a 10 m deep lake, the bottom is at a constant temperature of 4 °C. The air temperature is constant at -4 °C. The thermal conductivity of ice is 3 times that of water. Neglecting the expansion of water on freezing, what is the maximum thickness (in m) of ice that can be formed?
Ice will stop forming when :
Let is formed up to a depth of y and surface area of the lake is A, then
⇒ y = 7.5 m