1 litre of coffee at 80oC need to be cooled to 40oC. Assuming that all the ice melts and no heat is lost to the environment. Take the specific heat capacity of coffee to be 4200J/kgK, density of coffee to be 1000kg/m3 and latent heat of fusion of water to be 3.34 x 105 J/kg. You are required to:
a) Determine the heat lost by the coffee when ice is added and coffee cools to 40oC?
Solution:
To determine the heat lost by the coffee when ice is added and the coffee cools to 40oC, we need to consider the following steps:
Step 1: Calculate the initial heat content of the coffee:
The initial heat content of the coffee can be calculated using the formula:
Q1 = (mass of coffee) x (specific heat capacity of coffee) x (change in temperature)
Here, the mass of coffee = volume of coffee x density of coffee
The volume of coffee is 1 liter, which is equal to 1 kg (as the density of water is 1000 kg/m3)
Therefore, the mass of coffee = 1 kg
The specific heat capacity of coffee is given as 4200 J/kgK
The change in temperature is (40oC - 80oC) = -40oC
Substituting the values into the formula, we get:
Q1 = (1 kg) x (4200 J/kgK) x (-40oC)
Q1 = -168,000 J
Step 2: Calculate the heat content due to the melting of ice:
The heat content due to the melting of ice can be calculated using the formula:
Q2 = (mass of ice) x (latent heat of fusion of water)
Since all the ice melts, the mass of ice is equal to the mass of water formed.
The volume of water formed can be calculated by subtracting the volume of the ice (1 liter) from the volume of the coffee (1 liter).
Therefore, the volume of water formed = 1 liter - 1 liter = 0 liter
The mass of water formed = volume of water formed x density of water
The density of water is 1000 kg/m3, and the volume of water formed is 0 liter
Therefore, the mass of water formed = 0 kg
Substituting the values into the formula, we get:
Q2 = (0 kg) x (3.34 x 105 J/kg)
Q2 = 0 J
Step 3: Calculate the total heat lost by the coffee:
The total heat lost by the coffee is the sum of the heat lost due to the change in temperature and the heat lost due to the melting of ice.
Total heat lost = Q1 + Q2
Total heat lost = -168,000 J + 0 J
Total heat lost = -168,000 J
Therefore, the heat lost by the coffee when ice is added and the coffee cools to 40oC is -168,000 J.