A woman finds the front windshield of her car covered with ice at -12.6°C. The ice has a thickness of 4.80 10-4 m, and the windshield has an area of 1.25 m2. The density of ice is 917 kg/m3. How much heat is required to melt the ice?
Use the area, thickness, and density to calculate the mass of ice.
Then mass ice x specific heat ice x 12.6 = joules necessary to raise the temperature of the ice to zero degrees C. then add in the amount to melt the ice which is mass ice x heat of fusion. Watch the units. Post your work if you get stuck.
Why did the ice go to therapy? Because it was feeling a little melt-ted!
Now, let's calculate the amount of heat required to melt the ice using the formula:
Q = m * L
Where:
Q is the heat required
m is the mass of the ice
L is the latent heat of fusion of ice
First, let's calculate the mass of the ice:
Volume of ice = thickness * area
Volume of ice = (4.80 * 10^-4 m) * (1.25 m^2)
Volume of ice = 6 * 10^-4 m^3
Mass of ice = density * volume
Mass of ice = 917 kg/m^3 * 6 * 10^-4 m^3
Mass of ice = 5.502 kg
Now, let's calculate the heat required:
Q = 5.502 kg * (3.33 * 10^5 J/kg)
So, the amount of heat required to melt the ice is approximately Q = 183.1616 * 10^5 J. Keep in mind that this is just an approximation, but who needs precision when you have a good laugh, right?
To find the amount of heat required to melt the ice, we can use the formula:
Q = m * L
Where:
Q is the heat required
m is the mass of the ice
L is the latent heat of fusion of ice.
First, let's find the mass of the ice.
We can calculate the volume of the ice using the formula:
V = A * d
Where:
V is the volume of the ice
A is the area of the windshield
d is the thickness of the ice.
V = 1.25 m^2 * 4.80 x 10^-4 m
= 6 x 10^-4 m^3
Next, we can calculate the mass of the ice using the formula:
m = V * ρ
Where:
m is the mass of the ice
V is the volume of the ice
ρ is the density of ice.
m = 6 x 10^-4 m^3 * 917 kg/m^3
= 5.502 kg
Now, let's calculate the heat required using the formula:
Q = m * L
Where:
Q is the heat required
m is the mass of the ice
L is the latent heat of fusion of ice.
The latent heat of fusion of ice is typically given as L = 334,000 J/kg.
Q = 5.502 kg * 334,000 J/kg
≈ 1,835,668 J
Therefore, approximately 1,835,668 Joules of heat are required to melt the ice.
To calculate the heat required to melt the ice, we need to use the equation:
Q = m * L
where Q is the heat required, m is the mass of the ice, and L is the latent heat of fusion for ice.
To find the mass of the ice, we can use the formula:
m = ρ * V
where m is the mass, ρ is the density of ice, and V is the volume of the ice.
First, let's calculate the volume of the ice. The volume (V) can be determined using the formula:
V = A * h
where A is the area of the windshield and h is the thickness of the ice.
Now, let's calculate the volume of the ice:
V = 1.25 m^2 * 4.80 * 10^-4 m = 6 * 10^-4 m^3
Next, let's calculate the mass of the ice:
m = 917 kg/m^3 * 6 * 10^-4 m^3 = 5.502 kg
Finally, we need to find the latent heat of fusion for ice, which is the amount of heat required to change 1 kg of ice into water at 0°C. The latent heat of fusion for ice is 334,000 J/kg.
Now, let's calculate the heat required to melt the ice:
Q = m * L = 5.502 kg * 334,000 J/kg = 1,834,668 J
Therefore, the heat required to melt the ice is approximately 1,834,668 Joules.