You may have eaten “astronaut ice cream” as a kid at a science museum or planetarium to experience the type of food eaten by astronauts. Astronaut ice cream is made by chilling the ice cream to -40°C so that all of the water turns to ice. After freezing, the ice cream is subjected to vacuum and heat to sublimate (solid to vapor phase change) the ice and remove the water vapor through the vacuum pump. 75 kg/hr of ice cream (containing 40% by mass water) at -40°C is fed to the vacuum chamber. 98% of the water in the ice cream leaves the chamber as a vapor at 40°C and the rest of the water is a liquid, still with the “dried” ice cream, at 25°C. Calculate the required heat input for this process. You may assume that the vacuum pump work is very small compared to enthalpy and heat, and may be neglected in your energy balance. The heat capacity, Cp, of ice is 2.17 J/(g·°C) and the heat capacity Cp of ice cream (the non-water components) is 1.25 J/(g·°C). For simplicity, you may use only the first two terms of the heat capacity (a+bT) instead of the entire formula for water vapor and liquid.

Question
You may have eaten “astronaut ice cream” as a kid at a science museum or planetarium to experience the type of food eaten by astronauts. Astronaut ice cream is made by chilling the ice cream to -40°C so that all of the water turns to ice. After freezing, the ice cream is subjected to vacuum and heat to sublimate (solid to vapor phase change) the ice and remove the water vapor through the vacuum pump. 75 kg/hr of ice cream (containing 40% by mass water) at -40°C is fed to the vacuum chamber. 98% of the water in the ice cream leaves the chamber as a vapor at 40°C and the rest of the water is a liquid, still with the “dried” ice cream, at 25°C. Calculate the required heat input for this process. You may assume that the vacuum pump work is very small compared to enthalpy and heat, and may be neglected in your energy balance. The heat capacity, Cp, of ice is 2.17 J/(g·°C) and the heat capacity Cp of ice cream (the non-water components) is 1.25 J/(g·°C). For simplicity, you may use only the first two terms of the heat capacity (a+bT) instead of the entire formula for water vapor and liquid.

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