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1. Liquid nitrogen at −196° C (nitrogen’s boiling point) is placed in a container with 3...

1. Liquid nitrogen at −196° C (nitrogen’s boiling point) is placed in a container with 3 kg of water at 25° C. (a) Suppose you add just enough liquid nitrogen such that all the water just freezes (i.e., the final state of the water is ice at 0° C). Draw a complete energy interaction diagram for this scenario, including a conservation of energy equation.

(b) How much liquid nitrogen should you put in the container such that all the water just freezes? Nitrogen has a heat of vaporization of 199.1 kJ/kg, gaseous nitrogen has a specific heat of 1.04 kJ/(kg K), and water has a heat of melting of 333.5 kJ/kg and a specific heat of 4.18 kJ/(kg K). Assume the container is isolated from the environment.

(c) The molar specific heat of water vapor at constant pressure is 33.6 J/(mol K) (at room temperature). According to our model, how many active modes per water molecule does this correspond to?

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