To make ice cubes you fill am ice tray with 150g of water at 20°C. How much energy must be removed from the water to create ice cubes at a final temperature of -10C
heat removed:
cooling water to 0C: 150*cw*20
changing to ice: 150*heatfusionwater
cooling the ice to -10:
150(cice)(10)
add them up
To calculate the amount of energy that needs to be removed from the water, we can use the formula:
Q = mcΔT
Where:
Q is the amount of energy absorbed or released (in joules)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in joules per gram per degree Celsius)
ΔT is the change in temperature (in degrees Celsius)
First, let's convert the mass of the water from grams to kilograms:
m = 150g / 1000 = 0.15 kg
Next, let's calculate the energy required to cool the water from 20°C to 0°C:
Q1 = mcΔT = (0.15 kg)(4.186 J/g°C)(0 - 20°C) = -12.558 J
Now, let's calculate the energy required for the water to freeze at 0°C:
Q2 = mLf
Where:
Lf is the latent heat of fusion for water, which is 334 J/g
Q2 = (0.15 kg)(334 J/g) = 50.1 J
Finally, let's calculate the energy required to cool the ice from 0°C to -10°C:
Q3 = mcΔT = (0.15 kg)(2.093 J/g°C)(-10°C - 0°C) = -0.314 J
To determine the total amount of energy to be removed, we sum up the individual energy changes:
Total energy = Q1 + Q2 + Q3
Total energy = -12.558 J + 50.1 J - 0.314 J
Total energy = 37.228 J
Therefore, 37.228 joules of energy must be removed from the water to create ice cubes at a final temperature of -10°C.
To determine the amount of energy that needs to be removed from the water to create ice cubes at a final temperature of -10°C, we need to use the formula:
Q = m * c * ΔT
Where:
Q = amount of energy (in joules)
m = mass of water (in grams)
c = specific heat capacity of water (approximately 4.18 J/g°C)
ΔT = change in temperature (in °C)
First, let's calculate the total heat energy required to cool the water from 20°C to 0°C:
Q1 = m * c * ΔT1
Where:
m = 150g (mass of water)
c = 4.18 J/g°C (specific heat capacity of water)
ΔT1 = 0°C - 20°C = -20°C
Q1 = 150g * 4.18 J/g°C * -20°C
Next, we need to calculate the heat energy required to freeze the water at 0°C:
Q2 = m * L
Where:
m = 150g (mass of water)
L = latent heat of fusion for water (approximately 334 J/g)
Q2 = 150g * 334 J/g
Finally, we'll calculate the heat energy required to cool the ice from 0°C to -10°C:
Q3 = m * c * ΔT2
Where:
m = 150g (mass of water)
c = 2.09 J/g°C (specific heat capacity of ice)
ΔT2 = -10°C - 0°C = -10°C
Q3 = 150g * 2.09 J/g°C * -10°C
Now, we can calculate the total energy required by adding up Q1, Q2, and Q3:
Total energy = Q1 + Q2 + Q3
Note: Since we are dealing with specific heat capacities and latent heat, which have slightly different values depending on the temperature range, the final result may involve a small margin of error.