Calculate Thickness of Ice Sheet on Lake: -17.8°C in 3.80 Minutes

In summary, the air temperature at the surface of a lake is -17.8 °C with a 0.315-m-thick sheet of ice covering it. In 3.80 minutes, the ice thickens by approximately 0.0923 mm. Using the equation for heat transfer, the thickness was calculated based on the density, heat of fusion, thermal conductivity, and time. This calculation assumes that no heat is flowing from the ground below and that the added ice is very thin compared to the original thickness.
  • #1
rlc
128
1

Homework Statement


A 0.315-m-thick sheet of ice covers a lake. The air temperature at the ice surface is -17.8 °C. In 3.80 minutes, the ice thickens by a small amount. Assume that no heat flows from the ground below into the water and that the added ice is very thin compared to 0.315 m. Calculate the number of millimeters by which the ice thickens.

Homework Equations


Q = k A ΔT / d
dQ/dt = k∙A∙∆T/∆x
The heat of fusion of water is about 334 kJ / kg
k thermal conductivity, for ice k = 2.33 Wm⁻¹K⁻¹
A surface area of the lake
∆T temperature difference between the two sides of the ice sheet
∆x thickness of the ice sheet

The Attempt at a Solution


I've tried a bunch of different equations, but I'm missing something. Is that equation the one to use?
 
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  • #2
Never mind, I figured it out:
Density of ice=917 kg/m^3
Lf=33.5E4 J/kg
Thermal conductivity ice=2.2 J/smdegC

h=k(deltaT)t/pLfL
h=(2.2)(17.8)(228 secs)/(917)(33.5E4)(0.315)
h=9.2268E-5 m
Multiply by 1000 to get mm
0.0923 mm
 

Related to Calculate Thickness of Ice Sheet on Lake: -17.8°C in 3.80 Minutes

What is the formula for calculating the thickness of an ice sheet?

The formula for calculating the thickness of an ice sheet is: thickness = (temperature x time) / 9.8. This formula takes into account the temperature (in degrees Celsius) and the time (in minutes) it takes for the ice sheet to form, and uses the gravitational acceleration of 9.8 m/s^2.

What units should be used for the temperature and time in the formula?

The temperature should be in degrees Celsius, as this is the standard unit for measuring temperature in the SI system. The time should be in minutes, as this is the unit that is most commonly used when measuring the formation of ice sheets on lakes.

How accurate is the calculation of ice sheet thickness using this formula?

The accuracy of the calculation will depend on the accuracy of the temperature and time measurements. Small variations in these values can lead to significant differences in the calculated thickness. It is important to use precise measurement tools and record the values accurately to get a more accurate result.

Can this formula be used for calculating the thickness of ice sheets on any body of water?

This formula is specifically designed for calculating the thickness of ice sheets on lakes. The temperature and time values used in the formula may not be applicable to other bodies of water, such as oceans or rivers, as they have different temperatures and currents that can affect the formation of ice.

How does the thickness of an ice sheet on a lake affect its safety for activities like ice skating or fishing?

The thickness of an ice sheet on a lake is directly related to its safety for activities like ice skating or fishing. A thicker ice sheet indicates that the lake is more frozen and solid, making it safer for these activities. However, it is always important to check the thickness and quality of the ice before engaging in any activities on a frozen lake.

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