Question

The top of the lake is frozen. The air in contact with the surface of the lake is at \[ - {15^\circ}C\]. Then the maximum temperature of the water in contact with the lower surface of ice will be
A) \[ - {7.5^\circ}C\]
B) \[ - {4^\circ}C\]
C) \[{0^\circ}C\]
D) \[{4^\circ}C\]

Answer 1

Hint: In this question first of all we will describe how the ice form on the surface of lakes and then describe the conduction of heat through the ice and by using the concept that ice is an insulator of heat conduction we will give the required answer.

Complete step by step answer:
Given, the air in contact with the surface of the lake is at \[ - {15^\circ}C\].
Formation of Ice on the lakes:
In cold weather, we observe that ice is formed on the surface of lakes so here the question arises which phenomena are responsible for the formation of ice. When there is a cold the temperature of the atmosphere is below zero degrees Celsius. Since the heat always travels from higher temperatures to the lower temperature the molecules on the surface of lakes lose their heat which travels from molecules at higher temperatures to the atmosphere at a lower temperature so their intermolecular space reduces resulting in the formation of ice.
When the ice is formed on the lakes surface the thickness of ice keeps on increasing when the temperature outside the lakes decreases. Since ice is the insulator of heat transfer so no heat transfers take place after the formation of a thick layer of ice across it through its cross-sectional area. Hence the temperature inside the lakes does not change.
Since the minimum temperature at which water is in the liquid state is \[{4^\circ}C\].
Hence the maximum temperature of the water in contact with the lower surface of ice will be \[{4^\circ}C\]

Therefore, option (D) is correct.

Note:
It is important to note that the formation of ice on the lakes in the weather is very beneficial for the aquatic lives which prevent them from cold weather. The ice formed acts as a blanket for them.