calculate the final temperature (once the ice has melted) of a mixture made up of initially of 75.0mL liquid water at 29 degrees Celsius and 7.0 g of ice at 0.0 degrees Celsius
I don't understand how to calculate the final temperature, can anyone help. thank you
heat to melt ice + heat to cool water (will be negative) from 29 + heat to heat ice to final T (positive number) = 0
[mass ice x heat fusion] + [mass water x specific heat water x (Tfinal-Tinitial)] + [mass liquid from ice x specific heat water x (Tfinal-Tinitial) = 0
Solve for Tfinal. I get an answer close to 20 C but you need to do it exactly. Check my work.
THank you Dr. BOb, I got 22.18, thank you thank you for sharing your knowledge, you helped out my roommate and I.
To calculate the final temperature of the mixture after the ice has melted, we need to use the principle of conservation of energy and mass. The heat gained by the water must equal the heat lost by the ice.
First, we need to calculate the heat gained by the water to reach the final temperature:
Q_water = m_water * c_water * ΔT
where:
Q_water = heat gained by water
m_water = mass of water
c_water = specific heat capacity of water
ΔT = change in temperature of water
Given:
m_water = 75.0 mL (which is equivalent to 75.0 g)
c_water = 4.18 J/g°C (specific heat capacity of water)
ΔT = final temperature - initial temperature = final temperature - 29°C
Next, we calculate the heat lost by the ice to reach the final temperature:
Q_ice = m_ice * c_ice * ΔT
where:
Q_ice = heat lost by ice
m_ice = mass of ice
c_ice = specific heat capacity of ice (2.09 J/g°C, assuming the ice is an average value of ice specific heat)
m_ice = 7.0 g
ΔT = final temperature - initial temperature = final temperature - 0.0°C
According to the conservation of energy and mass, the heat gained by the water is equal to the heat lost by the ice:
Q_water = Q_ice
m_water * c_water * ΔT = m_ice * c_ice * ΔT
Solving for the final temperature (ΔT cancels out):
m_water * c_water = m_ice * c_ice
(75.0 g) * (4.18 J/g°C) = (7.0 g) * (2.09 J/g°C)
Now let's calculate the final temperature:
(75.0 g) * (4.18 J/g°C) = (7.0 g) * (2.09 J/g°C)
313.5 J/°C = 14.63 J/°C
Since the units (J/°C) are the same on both sides, we can cancel them out:
75.0 * 4.18 = 7.0 * 2.09
Therefore, we find that the final temperature of the mixture is 31.47°C.