Remember, we're trying to freeze the ice cream (not just cool it down), which is proportionally just as thermodynamically expensive as melting ice. Is it just

Remember, we're trying to freeze the ice cream (not just cool it down), which is proportionally just as thermodynamically expensive as melting ice. Is it just proportional, or is it actually pretty close to 1:1? That is, how accurate is the view that if you want to freeze 1L (or kg) of ice cream you need to melt 1L (or kg) of ice? Although I guess ice cream is not just frozen water, so perhaps that forms a fixed proportion. Alternatively stated, how much ice do you need to start with to freeze a given quantify of ice cream?