A bottle containing 4 kgof water at a temperature of 15°Cis placed in a refrigerator where the temperature is kept at 2°C.How much heat is transferred from the water to cool it to 2°C?
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To calculate the amount of heat transferred from the water to cool it to 2°C, we can use the formula:
Q = mcΔT,
where:
Q is the amount of heat transferred,
m is the mass of the water,
c is the specific heat capacity of water, and
ΔT is the change in temperature.
First, let's calculate the change in temperature:
ΔT = Tfinal - Tinitial,
where:
Tfinal is the final temperature (2°C), and
Tinitial is the initial temperature (15°C).
ΔT = 2°C - 15°C
ΔT = -13°C.
Next, we need to find the specific heat capacity of water. The specific heat capacity of water is approximately 4.18 J/g°C.
Now, we can substitute the values into the formula:
Q = (mass of water) × (specific heat capacity of water) × (change in temperature).
The mass of the water is given as 4 kg, but the specific heat capacity is given in grams. So, we need to convert the mass to grams:
mass of water = 4 kg × 1000 g/kg
mass of water = 4000 g.
Now, we can substitute the values and calculate the heat transfer:
Q = (4000 g) × (4.18 J/g°C) × (-13°C)
Q ≈ -217,840 J.
Note: The negative sign indicates that heat is transferred from the water to the refrigerator.