Evaporation Moisture: 0.3L/m2 Hot Water at 50°C

In summary, the problem is to determine the time it takes for 0.3 liters of hot water at 50 degrees Celsius to reach 0 degrees Celsius when poured on an ice rink at -5 degrees Celsius. The heat load can be calculated using the equation Heat load = 1000*0.3(liters/sm)*(4.2*(50-0)+333+2*(0-(-5)) and is equal to 165.9 kJ. The rate of evaporation can be calculated using the formula (mass loss rate)/(unit area) = (vapor pressure - ambient partial pressure)*sqrt( (molecular weight)/(2*pi*R*T) ) and the result is 0
  • #1
me1234
2
0

Homework Statement


- if I put 0.3 litres/squaremeter of hot water (50 C) on ice rink (-5 C), how long will take to the water to be 0 grade C ? How much evaporation moisture will be in the air (5 C) and how long will be the time for evaporation ?

Homework Equations


Heat load= 1000*0.3(liters/sm)*(4.2*(50-0)+333+2*(0-(-5))
Heat load=165.9 kJ
- evaporation heat of water =2270(kJ/kg)
so the moisture will be: 165.9/2270=0.07 kg


The Attempt at a Solution

 
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  • #2
I would start by assuming a thin layer of water above the ice, so that it's of uniform temperature but still with finite heat capacity. Then you have to use the conductivity of water and ice, latent heat of the latter, and specific heats of both, to determine the rate at which heat leaves the water layer. Not easy, since the ice is melting to some extent. (Eventually, all the water should wind up as ice even though the ambient temperature is +5C.)

Also, you should proably take into account the loss of heat of the water to radiatiion : eσ(T^4 - Ta^4) where Ta is +5 deg C and e for water has to be looked up (emissivity). T will vary from +50 to 0C.

As for rate of evaporation, the formula I found is
(mass loss rate)/(unit area) = (vapor pressure - ambient partial pressure)*sqrt( (molecular weight)/(2*pi*R*T) ). Has to be integrated since T is not constant. The rersult should give you both the amount of evaporate and the time to evaporate all the water.

This is a very complicated problem which may explain why you're not getting any responses from anybody else, and why mine is so flimsy. :-)

http://van.physics.illinois.edu/qa/listing.php?id=1440
 
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  • #3
Thank You very much
 

1. How does temperature affect evaporation of water?

As temperature increases, the kinetic energy of water molecules also increases. This causes them to move faster and escape the surface of the water, leading to a higher rate of evaporation.

2. Why does hot water evaporate faster than cold water?

Hot water has a higher temperature, which means its molecules have more energy and are able to break free from the surface and evaporate at a faster rate than cold water molecules.

3. How does the surface area of water affect evaporation?

The larger the surface area of water, the more molecules are exposed to the air and can escape as vapor. This means that water in a wide and shallow container will evaporate faster than water in a tall and narrow container.

4. What factors besides temperature affect the rate of evaporation?

Other factors that can affect the rate of evaporation include humidity, air flow, and air pressure. Higher humidity can slow down evaporation as there is already a lot of water vapor in the air, while low humidity can speed up evaporation. Air flow can carry away water vapor, also increasing the rate of evaporation. Changes in air pressure can also affect the rate of evaporation.

5. How does evaporation contribute to the water cycle?

Evaporation is a key part of the water cycle, where water from bodies of water, plants, and the ground evaporates into the air as water vapor. This water vapor then condenses to form clouds, which eventually lead to precipitation and the replenishment of bodies of water. This cycle ensures a continuous supply of water on Earth.

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