After a snow storm, your driveway of area 50m^2 is covered with a layer of ice 10cm high at a temperature of 0C. You decide to use sunlight falling at 200 W/m^2 to melt the ice? Is it good idea? (Density of ice is 920kg/m^3 and 1 cal = 4.184 J.
heat to melt ice : mass*Hf
= volume*density*Hf
= 50m^2*.1m*920kg/m^3)(4.18KJ/kg
= 19200kJ
energy available: 200W/m^2*50m^2*8hrs*3600sec/hr
= 28800kJ
The truth is, that intense sunlight doesn't exist through the day, as the sun rises and sets, it is much less, and the ice reflects a lot of energy.
check my calculations.
How long will it take to melt the ice?
How did you get the 8hrs and 3600 sec/hr??
60 sec/ min *60 min/hr = 3600 seconds/hour
He assumed 8 hours of daylight but as he said you will not get the full force for 8 hours.
To determine if using sunlight to melt the ice on your driveway is a good idea, we can calculate the amount of energy required to melt the ice and compare it to the energy provided by sunlight.
First, let's calculate the volume of ice on your driveway. Since the area is given as 50m^2 and the height of ice is given as 10cm (0.1m), the volume of ice can be calculated as follows:
Volume = Area x Height
Volume = 50m^2 x 0.1m
Volume = 5m^3
Next, using the density of ice (920kg/m^3), we can calculate the mass of the ice:
Mass = Density x Volume
Mass = 920kg/m^3 x 5m^3
Mass = 4600kg
To melt the ice, we need to calculate the amount of energy required. The specific heat capacity of ice is 2.09 J/g°C, which means it takes 2.09 Joules of energy to raise the temperature of 1 gram of ice by 1 degree Celsius.
Since the temperature of the ice is 0°C and it needs to be raised to the melting point of 0°C, no heat energy is required to change its temperature. We only need to consider the energy required for the phase change from solid to liquid:
Energy = Mass x Specific Heat Capacity x Temperature Change
Energy = 4600kg x 2.09 J/g°C x 0°C
Energy = 0 J
Therefore, no additional energy is required to raise the temperature of the ice to its melting point.
Now, let's calculate the energy provided by sunlight falling at 200 W/m^2. The energy delivered by sunlight per unit time can be calculated as follows:
Energy = Power x Time
Energy = 200 W/m^2 x Time
To find out how long it would take to melt the ice, we need to consider the effectiveness of sunlight in delivering energy to the ice. Some of the sunlight may be reflected or absorbed by other surfaces, reducing the amount of energy available to melt the ice. In this case, let's assume that 50% of the sunlight energy is absorbed by the ice:
Energy Absorbed = 200 W/m^2 x 0.5 x Time
To melt the ice, we need to deliver the energy calculated earlier (0 J). Setting the energy absorbed equal to the required energy, we can solve for time:
200 W/m^2 x 0.5 x Time = 0 J
Since any value multiplied by zero equals zero, we find that it would take an infinite amount of time for the ice to melt using sunlight falling at 200 W/m^2.
Therefore, it is not a good idea to rely solely on sunlight to melt the ice on your driveway. The amount of energy provided by the sunlight is not sufficient to melt the ice, even assuming perfect efficiency in energy absorption. Additional methods, such as using salt or mechanical means to break up the ice, would be more effective and efficient.