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 1cm of ice to be formed is 7 hours, then the time taken for the thickness of ice to change from 1cm to 2cm is:

• (A) 7 hours
• (B) 14 hours
• (C) 21 hours
• (D) 3.5 hours

To determine the time taken for the thickness of ice to change from 1 cm to 2 cm, we can use the principle of heat transfer and the relationship between temperature and ice formation. The rate of ice formation is generally proportional to the temperature difference between the water and the air.

Understanding Ice Formation

When the air temperature is significantly lower than the freezing point of water, ice forms more rapidly. In this case, the first 1 cm of ice takes 7 hours to form at an atmospheric temperature of -10°C.

Calculating the Time for Additional Thickness

As the ice thickens, the rate of heat loss decreases because the existing ice acts as an insulator. This means that the time taken to form the next layer of ice will be longer than the first. Typically, the time required to increase the thickness of ice doubles with each additional centimeter.

• First 1 cm: 7 hours
• Next 1 cm (from 1 cm to 2 cm): approximately 14 hours

Final Answer

The time taken for the thickness of ice to change from 1 cm to 2 cm is 14 hours. Therefore, the correct option is (B) 14 hours.