A 50.0- piece of ice at 0.0 is added to a sample of water at 8.0. All of the ice melts and the temperature of the water decreases to 0.0.
How many kilograms of water were in the sample?
(mass ice x heat fusion) + [Mass water x specific heat water x (Tfinal-Tinitial)] = 0
Solve for mass water and convert to kg.
To find the mass of water in the sample, we need to use the principle of conservation of energy.
First, let's calculate the heat gained by the ice as it melts. The heat gained can be found using the formula:
Q = m * L
Where Q is the heat gained, m is the mass of ice, and L is the latent heat of fusion for water, which is 334,000 J/kg.
Given that the mass of ice is 50.0 g (0.050 kg), we can calculate the heat gained:
Q = 0.050 kg * 334,000 J/kg = 16,700 J
This heat gained by the ice is equal to the heat lost by the water, according to the principle of conservation of energy. The heat lost by the water can be found using the formula:
Q = m * C * ΔT
Where Q is the heat lost, m is the mass of water, C is the specific heat capacity of water, and ΔT is the change in temperature of the water.
Let's rearrange this formula to solve for the mass of water:
m = Q / (C * ΔT)
Given that the heat lost is 16,700 J, the initial temperature of the water is 8.0°C, and the final temperature is 0.0°C, we can substitute these values into the formula:
m = 16,700 J / (4,186 J/kg · °C * (8.0 - 0.0) °C)
Simplifying this equation:
m = 16,700 J / (4,186 J/kg · °C * 8.0 °C)
m = 0.500 kg
Therefore, there were 0.500 kg (or 500 g) of water in the sample.
To solve this problem, we need to use the equation:
Q = m * c * ΔT
Where:
Q is the heat energy gained or lost by the substance (in this case, water and ice),
m is the mass of the substance,
c is the specific heat capacity of the substance, and
ΔT is the change in temperature.
Given:
Mass of ice (mice) = 50.0 g (or 0.050 kg)
Initial temperature of ice (Tice initial) = 0.0 °C
Final temperature of water (Twater final) = 0.0 °C
Initial temperature of water (Twater initial) = 8.0 °C
Let's calculate the heat energy gained or lost by the ice using the equation:
Qice = mice * cice * (Twater final - Tice initial)
Since the ice is melting, it needs to absorb heat energy from the water until its temperature reaches 0.0 °C. Therefore, the heat energy lost by the water can be calculated using the equation:
Qwater = mwater * cwater * (Twater final - Twater initial)
Since the final temperature of the water is the same as the initial temperature, it means there is no temperature change. Therefore, the equation becomes:
Qwater = mwater * cwater * 0
Since Qice = -Qwater (according to the conservation of energy), we can set these two equations equal to each other:
mice * cice * (Twater final - Tice initial) = -mwater * cwater * 0
Now we can solve for the mass of water (mwater):
mwater = (mice * cice * (Twater final - Tice initial)) / (cwater * 0)
Since any number divided by zero is undefined, it means the mass of water must be zero. However, this result seems unlikely because we know there is water present in the sample.
Therefore, there may be an error in the given values or assumptions. Please double-check the information and try again.