How much heat does a freezer need to remove from 1kg of water at 40°C to make ice at 0°C? (You will need to use the specific heat of water to drop the temperature first, before trying to make the phase change!) Show your work.
Please help! Also, this site isn't about giving out answers, so please don't, I just need help on how to find the answer. Thank you so much!
mass(specific heat * 40 + heat of fusion of water)
To find the amount of heat that needs to be removed from 1kg of water at 40°C to make ice at 0°C, we need to consider two steps: 1) heating water from 0°C to 0°C, and 2) phase change from liquid water to ice.
Step 1: Calculate the heat required to bring the 1kg of water from 40°C to 0°C using the specific heat capacity of water.
The specific heat capacity of water is approximately 4.186 J/g°C.
To calculate the heat required, we use the formula:
Q = m * c * ΔT
Where:
Q = heat energy
m = mass of the water (1kg)
c = specific heat capacity of water (4.186 J/g°C)
ΔT = change in temperature (0°C - 40°C = -40°C)
Converting the mass to grams:
m = 1kg * 1000g/kg = 1000g
Now we can calculate the heat required:
Q1 = 1000g * 4.186 J/g°C * (-40°C) = -167,440 J
Note that the negative sign indicates that heat energy is being removed from the water.
Step 2: Calculate the heat required for the phase change from liquid water at 0°C to solid ice at 0°C.
The heat of fusion (latent heat) for water is 334 J/g.
Using the formula:
Q2 = m * ΔHf
Where:
Q2 = heat energy
m = mass of the water (1kg)
ΔHf = heat of fusion of water (334 J/g)
Q2 = 1000g * 334 J/g = 334,000 J
Now we can find the total heat required for both steps:
Total heat = Q1 + Q2
Total heat = -167,440 J + 334,000 J = 166,560 J
Therefore, the freezer needs to remove 166,560 J of heat to convert 1kg of water from 40°C to ice at 0°C.
To find the amount of heat the freezer needs to remove from 1 kg of water at 40°C to make ice at 0°C, we need to consider two steps: first, we need to calculate the heat required to lower the temperature of the water from 40°C to 0°C, and then we need to calculate the heat required for the phase change from liquid to solid (ice) at 0°C.
Step 1: Calculating the heat required to lower the temperature:
To do this, we use the specific heat capacity of water. The specific heat capacity of water is approximately 4.18 J/g°C. Since we have 1 kg of water, we can convert the mass from kg to grams:
1 kg = 1000 grams
Now, we can calculate the heat required using the formula:
q = m * c * ΔT
Where:
q = heat energy
m = mass
c = specific heat capacity
ΔT = change in temperature
Plugging in the values, we have:
q = (1000 g) * (4.18 J/g°C) * (0°C - 40°C)
Simplifying the equation gives:
q = (1000 g) * (4.18 J/g°C) * (-40°C)
q = -167,200 J
So, the heat required to lower the temperature of 1 kg of water from 40°C to 0°C is -167,200 J.
Step 2: Calculating the heat required for the phase change:
To convert the water at 0°C to ice at 0°C, we need to use the heat of fusion. The heat of fusion for water is approximately 334 J/g.
Using the formula:
q = m * ΔH
Where:
q = heat energy
m = mass
ΔH = heat of fusion
Plugging in the values, we have:
q = (1000 g) * (334 J/g)
q = 334,000 J
So, the heat required for the phase change from liquid to solid (ice) at 0°C is 334,000 J.
To find the total heat the freezer needs to remove, we add the heat required for the temperature change to the heat required for the phase change:
Total heat = -167,200 J + 334,000 J
Total heat = 166,800 J
Therefore, the freezer needs to remove 166,800 J of heat from 1 kg of water at 40°C to make ice at 0°C.