Ice (initially at 0 degrees celcius)is added to 0.75 L of tea at 20 degrees celcius to make the coldest possible iced tea. If enough ice is added so the final mixture is all liquid, how much liquid is in the pitcher when this condition occurs?
To solve this problem, we need to determine the amount of ice that needs to melt to reduce the temperature of the tea to the point where all the ice has melted and there is only liquid left.
First, let's find the initial total heat content (enthalpy) of the tea. We can use the formula:
Q1 = m1 * c1 * ΔT1
Where:
Q1 = heat content of the tea
m1 = mass of the tea
c1 = specific heat capacity of the tea
ΔT1 = change in temperature of the tea
Given that the mass of the tea is 0.75 L and the specific heat capacity of water (which we can approximate for the tea) is about 4.18 J/g°C, and the change in temperature is 20°C (from 20 to 0 degrees Celsius), we can calculate Q1:
Q1 = 0.75 L * 1000 g/L * 4.18 J/g°C * 20°C
Next, let's find the heat content of the ice that needs to melt. The formula for this is:
Q2 = m2 * ΔHf
Where:
Q2 = heat content of the ice
m2 = mass of the ice
ΔHf = heat of fusion of ice
Since all the ice will eventually melt, the heat content of the ice needs to be equal to the heat content of the tea:
Q2 = Q1
By rearranging the equation, we can solve for m2 (mass of the ice):
m2 = Q1 / ΔHf
The heat of fusion of ice, ΔHf, is approximately 334 J/g.
Substituting the values into the equation:
m2 = Q1 / 334 J/g
Now we can calculate the mass of the ice that needs to melt. To convert the mass of ice to volume, we need to know the density of ice. The density of ice is approximately 0.92 g/mL.
Let's find the mass and volume of the ice:
mass of ice = m2
volume of ice = mass of ice / density of ice
To determine how much liquid is left after all the ice has melted, we subtract the volume of ice from the initial volume of the tea:
volume of liquid = initial volume of tea - volume of ice
Given that the initial volume of tea is 0.75 L, we can calculate the volume of liquid left.
By working through these calculations, you should be able to determine the volume of liquid in the pitcher when all the ice has melted.