In 2002, a gargantuan iceberg broke away from the Ross Ice Sheet in Antarctica. It was approximately a rectangle 218 km long, 25.0 km wide, and 250.0 m thick. What is the mass of this iceberg, given that the density of ice is 917 kg/m3? How much heat transfer (in joules) is needed to melt the iceberg? How many years would it take sunlight alone to melt ice this thick, if the ice absorbs an average of 105 W/m2, 12.0 hours per day?
The answers to the first 2 questions are 1.249*10^15kg and 4.173*10^20J. I just need the answer to how many years it'd take for the sun to melt the ice.
heat of fusion (melting) for ice is ... 334 J/g
unit energy absorption is ... 105 J/s m^2
... multiply by the area to find total energy absorption rate
divide the mass of the ice by the heat of fusion to find total energy of melting
divide the total melting energy by the total energy absorption rate
... to find the melting time
... remember, only 12 hr per day
I got 46.2
To find out how many years it would take for the sun to melt the ice, we need to calculate the amount of heat energy required to melt the iceberg and then determine how long it would take for the sun to provide that much energy.
First, let's calculate the total mass of the iceberg:
Mass = Density x Volume
Density of ice = 917 kg/m^3
Volume = Length x Width x Thickness
Length = 218 km = 218,000 m
Width = 25.0 km = 25,000 m
Thickness = 250.0 m
Volume = 218,000 m x 25,000 m x 250.0 m
Now we can calculate the mass:
Mass = 917 kg/m^3 x (218,000 m x 25,000 m x 250.0 m)
The mass of the iceberg is approximately 1.249 x 10^15 kg.
Next, let's calculate the amount of heat energy required to melt the iceberg. The heat energy required to melt a substance is given by the formula:
Heat Energy = Mass x Specific Heat Capacity x Change in Temperature
In this case, the change in temperature is from the melting point of ice (0 degrees Celsius) to the freezing point of water (0 degrees Celsius), which means there is no temperature change.
Specific Heat Capacity of ice = 2.09 J/g°C = 2090 J/kg°C
Heat Energy = Mass x Specific Heat Capacity x Change in Temperature
Heat Energy = 1.249 x 10^15 kg x 2090 J/kg°C x 0°C
The heat transfer required to melt the iceberg is approximately 4.173 x 10^20 J.
Now, let's calculate how many years it would take for the sun alone to melt the ice, considering the ice absorbs an average of 105 W/m^2 for 12.0 hours per day.
To do this, we need to calculate the total energy provided by the sun and then divide it by the energy required to melt the ice.
Energy provided by the sun = Power absorbed by the ice x Time
First, let's calculate the power absorbed by the ice:
Power absorbed by the ice = Area x Power per unit area
Area = Length x Width
Length = 25.0 km = 25,000 m
Width = 250.0 m
Area = 25,000 m x 250.0 m
Next, calculate the power absorbed by the ice:
Power absorbed by the ice = Area x Power per unit area
Power absorbed by the ice = (25,000 m x 250.0 m) x 105 W/m^2
Now we can calculate the energy provided by the sun:
Energy provided by the sun = Power absorbed by the ice x Time
Time = 12.0 hours per day = 12.0 hours x 3600 seconds/hour
Energy provided by the sun = (25,000 m x 250.0 m) x 105 W/m^2 x (12.0 hours x 3600 seconds/hour)
The energy provided by the sun is approximately 3.9375 x 10^16 J.
Finally, let's calculate how many years it would take for the sun alone to melt the ice:
Years = Energy required to melt the ice / Energy provided by the sun
Years = 4.173 x 10^20 J / 3.9375 x 10^16 J
The number of years required for the sun alone to melt the ice is approximately 10,597 years (assuming continuous energy absorption and neglecting any heat loss).