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What happens when you add salt to the ice bath in an ice cream maker? How is it possible for the temperature to spontaneously drop below 0"C? Explain in as much detail as you can.

Short Answer

Expert verified

The ice cream bath is always below 0 degrees Celsius.

Step by step solution

01

Given information

Add salt to the ice bath in an ice cream maker.

02

Explanation

We know that water turns to the ice (solid) phase at 0°C, but the temperature of the ice bath must be less than 0°C, which can be accomplished by adding salt to the ice bath system. Adding salt to the ice bath system lowers the phase temperature, resulting in a lower transition temperature between the phases. The kinetic energy of the particles in the mixture determines the temperature of the mixture, and as the kinetic energy reduces, the temperature of the mixture decreases.

03

Explanation

The ice cream and salt mixture are insulated from the environment in the ice cream making system, which means that the energy required to break the chemical bonds of the salt crystal must be taken from the kinetic energy of the mixture particle, resulting in a decrease in kinetic energy and thus the temperature. As a result, the ice cream bath is always below 0 degrees Celsius.

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Most popular questions from this chapter

Problem 5.58. In this problem you will model the mixing energy of a mixture in a relatively simple way, in order to relate the existence of a solubility gap to molecular behaviour. Consider a mixture of A and B molecules that is ideal in every way but one: The potential energy due to the interaction of neighbouring molecules depends upon whether the molecules are like or unlike. Let n be the average number of nearest neighbours of any given molecule (perhaps 6 or 8 or 10). Let n be the average potential energy associated with the interaction between neighbouring molecules that are the same (4-A or B-B), and let uAB be the potential energy associated with the interaction of a neighbouring unlike pair (4-B). There are no interactions beyond the range of the nearest neighbours; the values of μoandμABare independent of the amounts of A and B; and the entropy of mixing is the same as for an ideal solution.

(a) Show that when the system is unmixed, the total potential energy due to neighbor-neighbor interactions is 12Nnu0. (Hint: Be sure to count each neighbouring pair only once.)

(b) Find a formula for the total potential energy when the system is mixed, in terms of x, the fraction of B.

(c) Subtract the results of parts (a) and (b) to obtain the change in energy upon mixing. Simplify the result as much as possible; you should obtain an expression proportional to x(1-x). Sketch this function vs. x, for both possible signs of uAB-u0.

(d) Show that the slope of the mixing energy function is finite at both end- points, unlike the slope of the mixing entropy function.

(e) For the case uAB>u0, plot a graph of the Gibbs free energy of this system

vs. x at several temperatures. Discuss the implications.

(f) Find an expression for the maximum temperature at which this system has

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(g) Make a very rough estimate of uAB-u0for a liquid mixture that has a

solubility gap below 100°C.

(h) Use a computer to plot the phase diagram (T vs. x) for this system.

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(b) At what temperature is exactly half of the hydrogen ionised?

(c) Would raising the initial pressure cause the temperature you found in part (b) to increase or decrease? Explain.

(d) Plot the expression you found in part (a) as a function of the dimension- less variable t = kT/I. Choose the range of t values to clearly show the interesting part of the graph.

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