# How much liquid nitrogen (at its boiling point of - -196°C) is ...

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How much liquid nitrogen (at its boiling point of - -196°C) is needed to make 225 mL of ice cream? We are going to assume that this is a premium ice cream with a density of 0.850 g/mL. We will start with a liquid mixture of cream, sugar, etc. that has a freezing point of -3.5°C. Our ice cream mixture is initially in a steel bowl that has a mass of 0.400 kg. The bowl and mixture are at 1.0°C, initially. To be able to be served as ice cream, the mixture must be cooled to - -12.0°C. (Possibly useful information: specific heat of liquid ice cream mixture, 3.50 X J/(kg-°C); specific heat of frozen ice cream, 1.75 X 10³ J/(kg-°C); specific heat of steel: 502 J/(kg-°C); latent heat of fusion of steel, 2.90 X 105 J/kg; latent heat of fusion of ice cream mixture, 2.10 X 105 J/kg; latent heat of fusion of nitrogen, 2.55 X 104 J/kg; latent heat of vaporization of nitrogen, 2.01 X 105 J/kg) What mass (in kg) of liquid nitrogen at - -196°C will be needed to turn our 1.0°C liquid ice cream mixture in a 0.400 kg steel bowl (also at 1.0°C into 225 mL of ice cream at - -12.0°C? The bowl and ice cream stay in thermal contact throughout the problem. Assume no other heat is added or escapes to the environment.

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