If i place a dish of ice outside in the sun, The ice has a mass of 0.59 kg and a surface area of 0.039 m2. Assuming that the ice is originally at 0 °C and using my answer for part b, which was 1370w/m^2 * 49 * 0.039m^2 = 26.18 watts, How long do i have to wait until all the ice is melted and the temperature of the resulting water has reached 4.5 °C?
You may assume that the specific heat capacity of water, c, is
4.2 × 103 J kg−1 °C−1 and that the specific latent heat of melting of water, Lf, is 3.3 × 105 J kg−1 .
hoping that one of physics experts might pick it up.
To determine the time required for all the ice to melt and the resulting water to reach 4.5°C, we need to calculate the total energy required for this process.
1. First, let's calculate the total energy required to raise the temperature of the ice from 0°C to 4.5°C. We can use the equation:
Q = mcΔT
Where:
Q is the energy needed,
m is the mass of the ice,
c is the specific heat capacity of water,
ΔT is the change in temperature.
Given:
m = 0.59 kg
c = 4.2 × 10^3 J kg^(-1) °C^(-1)
ΔT = 4.5°C - 0°C = 4.5°C
Q = (0.59 kg) × (4.2 × 10^3 J kg^(-1) °C^(-1)) × (4.5°C)
Q = 11,489.5 J
So, it requires 11,489.5 joules of energy to raise the ice from 0°C to 4.5°C.
2. Next, let's calculate the total energy required to melt the ice. We can use the equation:
Q = mLf
Where:
Q is the energy needed,
m is the mass of the ice,
Lf is the specific latent heat of melting of water.
Given:
m = 0.59 kg
Lf = 3.3 × 10^5 J kg^(-1)
Q = (0.59 kg) × (3.3 × 10^5 J kg^(-1))
Q = 194,700 J
So, it requires 194,700 joules of energy to melt the ice.
3. Now, let's calculate the total energy required for the whole process by adding the energy for temperature change and the energy for melting:
Total Energy = Energy for Temperature Change + Energy for Melting
Total Energy = 11,489.5 J + 194,700 J
Total Energy = 206,189.5 J
4. We already know the power received by the ice from part b, which is 26.18 watts. To determine the time required, we can use the formula:
Time (t) = Total Energy (Q) / Power (P)
t = 206,189.5 J / 26.18 W
t = 7,876.79 seconds
Therefore, you would have to wait approximately 7,877 seconds or 2 hours and 11 minutes for all the ice to melt and the resulting water to reach 4.5°C.