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Anomalous Expansion of Water

If y is the i...

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If y is the instantaneous thickness of ice formed on the surface of a lake in winter than the rate of formation of ice is directly proportional to 1 ) y 2) y^2 3) 1/y 4) 1/y^2

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Q. On a winter day when the atmospheric temperature drops to −10°C, ice forms on the surface of a lake. (a) Calculate the rate of increase of thickness of the ice when 10 cm of the ice is already formed. (b) Calculate the total time taken in forming 10 cm of ice. Assume that the temperature of the entire water reaches 0°C before the ice starts forming. Density of water = 1000 kg m⁻³, latent heat of fusion of ice = 3.36 × 10⁵ J kg⁻¹ and thermal conductivity of ice = 1.7 W m⁻¹°C⁻¹. Neglect the expansion of water of freezing.

Q. A lake surface is exposed to an atmosphere where the temperature is less than

0^{o} C

. If the thickness of the ice layer formed on the surface grows from

2 c m

4 c m

1

hour, the atmosphere temperature will be (Thermal conductivity of ice,

K = 4 \times 10^{- 3} c a l c m^{- 1} s^{- 1}^{o} C^{- 1}

, density of ice

= 0.9 g c c^{- 1}

. Latent heat of fusion of ice

= 80 c a l g^{- 1}

Neglect the change of density during the state change. Assume that the water below the ice has

0^{o} C

temperature every where.)

Q. A lake surface is exposed to an atmosphere where the temperature is less than

0

. If the thickness of the ice layer formed on the surface grown from 2 cm to 4 cm in 1 hour, the atmospheric temperature will be (Thermal conductivity office,

K = 4 \times 10^{- 3} c a l {c m}^{- 1} s^{- 1}^{- 1}

, density of ice

0.9 g {c c}^{- 1}

. Latent heat of fusion of ice

80 c a l g^{- 1}

Neglect the change of density during the state change. Assume that the water below the ice has

0

temperature every where.)

Q. Ice starts forming on the surface of a lake and takes

8

hours to form a layer of

1

cm thickness. How much time will it take to increase the thickness of the layer to

2

Q. A lake is covered with ice and the atmospheric temperature above the ice is

- 10^{\circ} C

. Find the rate of formation of ice

(in cm/hr)

when its thickness is

5 cm

.
[Thermal conductivity of ice

= 0.005 cgs

units, density of ice

= 0.9 g/cc

and latent heat of fusion of ice

= 80 cal/g

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