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This device is used to "slush-freeze" concentrated orange juice. The juice (yellow) is pumped through the inner annulus. A shaft passes the length of that tube with a spiral scraper attached.
Ammonia is the

usual refrigerant.

As ammonia (blue) passes through the outer annulus it causes the juice to freeze to the inside wall of its path. The scraper, rotated by a motor, forces the liquid/solid concentrate to exit upper left.

**Calculate** the least steady mass rate of ammonia required by the device.

♦ The system will be the orange juice approximated as water and the ammoonia. The OJ enters as liquid and leaves, part solid-part liquid. The proportion is given by the exiting quality, **x**_{sf} (where **s** means solid and **f** means liquid). Quality is the ratio of the mass of the "higher energy" phase divided by the mass of both phases present. The order of energy among phases is: gas - greatest, next liquid and least energetic is the solid phase.

The event is steady and the "least" ammonia flow rate is associated with no heat from the surroundings (that wastes the ammonia). The energy equation, with the reductions is:

(1) 1 |

We have two flow streams: water and ammonia. We neglect their potential and kinetic energy changes. Surely these are smmall:

(2) 2 |

We check this equation again. Of the properties to enter, ammonia ia the easier. The ammonia changes phase from liquid to vapor so "in" is liquid (f) and "out" is vapor (g).

(3) 3 |

The water enters as saturated liquid. The exiting flow is 88% solid and 12% liquid.

(4) 4 |

Putting these numbers in the energy equation with the motor power gives:

(5) 5 |

Again, our numbers are approximate. The very cold temperature will enhance heat from the surroundings.