Physics???

When the air temperature is below 0 C, the water at the surface of a lake freezes to form a sheet of ice.

If the upper surface of an ice sheet 24.2 cm thick is at -10.7 C and the bottom surface is at 0.00 C, calculate the time it will take to add 1.80 mm to the thickness of this sheet.

(2.42cm=.0242m)
(1.80mm=.00180m)

I don't have any equations with time in my notes, any ideas????

  1. 👍 0
  2. 👎 0
  3. 👁 70
asked by Chels
  1. if anyone checks this-please help!!!! please!!

    1. 👍 0
    2. 👎 0
    posted by Chels
  2. bnbn

    1. 👍 0
    2. 👎 0
  3. Assume that the freezing of an additional layer is slow enough. Then the temperature profile can be assumed to be linear across the layer of ice. This quasistatic assumptions allows us to solve this problem without the need of solving the much more difficult moving boundary condition.

    The amount of heat that leaves the top surface has two origins: the latent heat of freezing of the additional sheet of water at the bottom plus the heat from additional cooling of the existing ice.
    This will give a heat balance equation from which a "thickness goes as sqrt(time) " formula emerges.

    First, the linear temperature profile assumed is (meauring thickness x from the top surface downwards)

    T = T0 + x delta(T)/d

    The energy balance is for infinitesimal time delta(t) is

    k (delta(T)/d) delta(t) = rho L delta(d) + integral_0^d rho sigma delta(T) dx

    d is the thickness of the sheet (distance of growth)
    With the linear profile this gives

    d(t) ^2 = d(0)^2 + t * 2 k delta(T)/( rho L + 1/2 rho sigma delta(T) )

    Here k is the conductivity of ice, L the latent heat of melting, rho the density of ice and delta(T) the temperature difference between top and bottom.

    From this you can calcute the time it takes to grow an additional 2.10 mm on 24.6 cm.
    Just solve for t with d(0) = 0.246 m and d(t) = 0.2481 m

    1. 👍 0
    2. 👎 0
    posted by cool

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A primitive diving bell consists of a cylindrical tank with one end open and one end closed. The tank is lowered into a freshwater lake, open end downward. Water rises into the tank, compressing the trapped air, whose temperature

    asked by Jason on November 11, 2014
  2. physics

    A primitive diving bell consists of a cylindrical tank with one end open and one end closed. The tank is lowered into a freshwater lake, open end downward. Water rises into the tank, compressing the trapped air, whose temperature

    asked by kb on November 19, 2008
  3. Physics

    A swimmer has 8.20 x 10^-4 m^3 of air in his lungs when he dives into a lake. Assuming the pressure of the air is 95 percent of the external pressure at all times, what is the volume of the air at a depth of 10.0 m? Assume that

    asked by Jim on April 1, 2008
  4. physics

    A snow maker at a resort pumps 260 kg of lake water per minute and sprays it into the air above a ski run. The water droplets freeze in the air and fall to the ground, forming a layer of snow. If all of the water pumped into the

    asked by Anonymous on November 25, 2013
  5. physics

    Assume all temperatures to be exact, and neglect significant figures for small changes in dimension. A diver releases an air bubble of volume 4.0cm3cm^3 from a depth of 16mm below the surface of a lake, where the temperature is

    asked by Rich on December 6, 2014
  6. Physics

    At a height of 15 meters above the surface of a lake, a sound pulse is generated. The echo from the bottom of the lake returns to the point of origin 0.150 s later. The air and water temperatures are 20°C. How deep is the lake?

    asked by Kristina on February 11, 2011
  7. science (physic)

    An expansible ballon filled with air floats on the surface of a lake with 2/3 of its volume submerged .How deep must it be sunk in the water so that it is just inequilibrium neither sinking further nor rising? It is assumed that

    asked by Aryan on January 22, 2017
  8. AP Physics

    At a height of 5 meters above the surface of a freshwater lake, a sound pulse is generated. The echo from the bottom of the lake returns to the point of origin 0.140 s later. The air and water temperatures are 20°C. How deep is

    asked by Alan on February 9, 2011
  9. Physics

    A sound wave travels in air toward the surface of a freshwater lake and enters into the water. The frequency of the sound does not change when the sound enters the water. The wavelength of the sound is 3.52 m in the air, and the

    asked by Abdul on April 9, 2018
  10. Physics

    A bubble of air, 0.010 m^3 in volume, is formed at the bottom of a lake which is 30.0 m deep and where the temperature is 8.0 C. The bubble rises to the surface, where the water temperature is 26 C and where the pressure is

    asked by Anonymous on December 11, 2012

More Similar Questions