- #1
waltssillyhat
- 5
- 1
- Homework Statement
- this is a multi-part question from my textbook: "It is possible to make home-made ice cream by using a salt-water solution (brine) as a refrigerant for the cream and sugar mix. You can assume for the purposes of this exercise that the cream and sugar mix is 70% water. It is actually the water in the cream that freezes. Salt is added to ice to make 5.00 kg of cold brine at−11°C. 500 g of cream and sugar mixture is cooled in a plastic bag which is plunged into the refrigerant."
we have been given the following information:
Heat of fusion of water: 334 kJ kg−1
Specific heat capacity of water: 4200 J kg−1 K−1
Specific heat capacity of cream and sugar mix: 3.80 × 103 J kg−1 K−1
Specific heat capacity of brine solution: 3.5 × 103 J kg−1 K−1
i have found the first few parts of the question, which are the amount of heat extracted from the ice cream mixture to decrease its temperature to 0 degrees (47.5kJ) and the the heat that needs to be removed for the 70% of water in the mixture to freeze (116.9 kJ). the final part of the question asks "Calculate the final temperature of the mixture when all the water in the ice cream is frozen, assuming no other heat loss", which is where I am struggling.
- Relevant Equations
- Q = mcΔt and Q = m x Lfusion
I tried to set the total amount of heat extracted from the mixture (-116.9 + (-47.5) = -164.4 kJ) equal to mcΔt of the ice cream mixture and solve for the final temperature, but my answer was wrong. I'm just not really sure when to use the specific heat capacity of the brine solution. I was thinking of setting mcΔt of the brine solution and mcΔt of the ice cream mixture together and solving for the final temperature, but I would have to calculate the final temperature of the brine solution and I feel like this just complicates the question. By the way, the answer to the question is -1.6 degrees celsius. Any help is appreciated :)
