a 42 piece of ice at 0.0 C is added to a sample of water at 8.0 C. all of the ice melts and the temperature of the water decreases to 0.0 C. how many grams of water were in the sample.
To find the number of grams of water in the sample, we need to use the concept of heat transfer and the principle of energy conservation.
Let's start by determining the amount of heat that is transferred when the ice melts. The heat transferred can be calculated using the formula:
Q = m * L
Where:
Q is the heat transferred (in Joules)
m is the mass of the ice (in grams)
L is the latent heat of fusion for water (in Joules per gram)
The latent heat of fusion for water is 334 J/g.
Given that the mass of the ice is 42 grams, we can calculate the heat transferred:
Q = 42 g * 334 J/g = 14028 J
Next, we need to determine the amount of heat that is lost by the water as it cools down. The heat lost can be calculated using the formula:
Q = m * c * ΔT
Where:
Q is the heat transferred (in Joules)
m is the mass of the water (in grams)
c is the specific heat capacity of water (in Joules per gram per degree Celsius)
ΔT is the change in temperature (in degrees Celsius)
The specific heat capacity of water is 4.18 J/g°C.
We know that the initial temperature of the water is 8.0°C, and the final temperature is 0.0°C. Therefore, the change in temperature is:
ΔT = 0.0°C - 8.0°C = -8.0°C
We can now calculate the heat lost:
Q = m * c * ΔT
14028 J = m * 4.18 J/g°C * (-8.0°C)
To isolate the mass, we rearrange the equation:
m = 14028 J / (4.18 J/g°C * (-8.0°C))
m ≈ 420 g
Thus, the mass of the water in the sample is approximately 420 grams.