When you go out to your car one cold winter morning you discover a 0.54 cm thick layer of ice on the windshield, which has an area of 1.6 m2. If the temperature of the ice is -4.1°C, and its density is 917 kg/m3, find the heat required to melt all the ice. Express your answer with three significant digits.
___MJ
PLEASE HELP!
Heat=massice*cice*(4.1)+massice*Hfice
massice=volumeice*densityice=area*thickness*density.
What is cice and Hfice on here?
mass of ice
To find the heat required to melt all the ice, we need to calculate the amount of heat needed to raise the temperature of the ice from -4.1°C to its melting point at 0°C, and then the heat required to melt the ice completely.
First, let's calculate the amount of heat required to raise the temperature of the ice. We can use the specific heat capacity formula:
Q = mcΔT
Where:
Q is the heat (in joules)
m is the mass of the ice (in kilograms)
c is the specific heat capacity of ice (in J/kg°C)
ΔT is the change in temperature (in °C)
The mass of the ice can be calculated using the density formula:
density = mass / volume
Rearranging the formula, we get:
mass = density x volume
Given that the density of the ice is 917 kg/m^3 and the volume is the area of the windshield multiplied by the thickness of the ice, we can calculate the mass of the ice.
mass = density x volume
mass = 917 kg/m^3 x (1.6 m^2 x 0.54 cm)
Since the thickness of ice is given in centimeters, we need to convert it to meters:
0.54 cm = 0.54/100 m = 0.0054 m
mass = 917 kg/m^3 x (1.6 m^2 x 0.0054 m)
Now you can calculate the mass of the ice.
Next, we need to calculate the change in temperature (ΔT) from -4.1°C to 0°C.
ΔT = final temperature - initial temperature
ΔT = 0°C - (-4.1°C)
Now that we have the mass and the change in temperature, we can calculate the heat required to raise the temperature of the ice:
Q1 = mcΔT
After calculating Q1, we can move on to the second part, which is calculating the heat required to melt the ice. We can use the latent heat formula:
Q2 = mL
Where:
Q2 is the heat required to melt the ice (in joules)
m is the mass of the ice (in kilograms)
L is the latent heat of fusion for ice (in J/kg)
The latent heat of fusion for ice is a constant value, which is 334,000 J/kg.
Calculating Q2 will give us the heat required to melt the ice completely.
Finally, we can calculate the total heat required by adding Q1 and Q2:
Total heat = Q1 + Q2
Remember to express your answer with three significant digits and convert it from joules (J) to megajoules (MJ) by dividing the value by 1,000,000.