Thermal and statistical physics: 6. Air conditioner usually works by consuming e

Question

Thermal and statistical physics:

6. Air conditioner usually works by consuming electric energy. Is it possible to design an air conditioner receiving energy from lukewarm water, which is colder than outside air, but warmer than your desired room temperature? To address this question, suppose the air temperature outside is To, while you want to maintain a temperature TT To in the room, and you have a source of water at some temperature Tw intermediate between To and Tr To Tw TT. How would you characterize the efficiency of such a device? What does fundamental physics have to say about this efficiency? Extra credit question (1 point): Given the three temperatures To, Tr, and Tw and nothing else, is it possible to find how much water per minute will be needed?

Explanation / Answer

now first thing is the basic concept of air condinitoner . All our physical laws of thermodynamics tell us that in equilibrium there is no heat transfer among systems and that means net work done is zero. without heat trasfer we cantnot change the temperature. Therefore we need one hot body and another cold body for heat trasfer and changing the internal energy. Per 1st law of thermodynamics change in U= Q-W

usually aiming equilibrium hot body transfer heat to the cold body but we need a cooling effect in our room that means we have to do the opposite or transfer heat from cold to hot body.This is a forced condition and we need an external force to do that. In this case Tw is greater than Tr and T0 is gretater than Tw and we have to maintain Tr. That means our air conditioner works on two principles.

First of all the lukewarm source will stop heat trasfer from room to make it cold.

secondly the source will stop taking heat from outside /T0

again we have to consider the entropy.

that means we need condenser, evaporator and compressor.

air to lukewarm source:

In this case it takes heat from outside by evaporator and using compressor creates the entropy. Finally taking condenser the hot air is cooled.

lukewarm source to room:

the cooled air in the source has high temperature than room therefore another condenser will cool the air and let it flow in the room via compressor.

Therefore total efficiency= power output/power input

or efficiency =evaporator power+compressor power/(condeser1power+condenser2power+compressor2power)

that means according to carnot theorem the space cooling procedure is troublesome as in the second process the condenser have to maintain a particular temperature.

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