# Homework Help: Carnot engines and refrigerators

1. Sep 27, 2008

### emperrotta

1. The problem statement, all variables and given/known data
I am not necessarily having a problem with a particular homework problem. It is more of a conceptual issue. I have been reading about Carnot engines and refrigerators. In trying to understand the topic better, I did a little more digging and looked up how a refrigerator actually works. There is one aspect that I am not really understanding, and that is how does the compressor of a refrigerator in compressing the gas form of the refrigerant cause the temperature of the compressed gas to increase? Also, how does pressurizing the gas allow it to condense into a liquid as it starts releasing heat into the environment outside the refrigerator even though the temperature it ends up at after releasing heat is still way above its boiling point?

2. Relevant equations

3. The attempt at a solution
My best guess is that the compressor does work on the refrigerant by decreasing the volume that the gas occupies and pressurizing it, which adds to the internal energy of the refrigerant and this causes the temperature to increase. As for my second question, my guess is that since the molecules have been forced into this small volume and heat is being released, the molecules being compacted into this tight space start to bond with each other forming a liquid.

Last edited: Sep 27, 2008
2. Sep 28, 2008

### whyhello112

Re: refrigerators

This concept is derived from the ideal gas law stating that the the pressure times volume equals number of atoms time the gas constant times temperature (PV=nRT). Dividing by T on both sides gives PV/T=nR which is a constant for a closed system such as a refrigerator. Therefore the quantity of PV/T is equal to that of state, (PV/T)1=(PV/T)2 (sorry i don't can't figure out how to post subscripts, the 1 and 2 are subscripts). So if you raise the pressure from an initial state, the volume must go down, or the temperature must go up, or both (other aspects of the problem will specify exactly).
As for the condensation, the state of matter depends on pressure and temperature. A higher pressure means a higher boiling point and. The refrigerator compresses the gas to a pressure where the temperature is below the boiling point.

3. Sep 28, 2008

### Andrew Mason

Re: refrigerators

This is a good question.

PV=nRT does not explain why T should increase if V decreases while P increases. The increase in temperature has to do with the fact that compression adds energy to the gas.

T is a measure of the average energy of the gas molecules. During adiabatic compression (no heat flows into or out of gas so Q = 0), the only increase in energy of the gas is due to the work done on the gas. Applying the first law (conservation of energy), $\Delta Q = \Delta U + W$ it is apparent that $\Delta U = -W$. Since work done by the gas, W, is negative, this means that the internal energy $\Delta U$ must increase. This means the molecular speed of the gas molecules increases, which is just a measure of temperature.

Physically, one can see how the movement of the container walls inward adds kinetic energy to molecules that collide with that wall. That means T increases. If walls are expanding, the molecules will rebound with less energy, so as volume increases T will decrease. (I am referring to adiabatic processes where Q = 0).

AM

4. Sep 28, 2008

### emperrotta

Re: refrigerators

How does increasing the pressure of a gas increase the boiling point of the gas?

5. Sep 29, 2008

### Andrew Mason

Re: refrigerators

I think you mean how does an increase of the external atmospheric pressure increase the boiling point of a liquid that it is in contact with?

What is the definition of "boiling point"? (Think in terms of the relationship between vapour pressure of the liquid and external pressure). What is the vapour pressure determined by (think in terms of translational kinetic energy of the molecules in the liquid)? If you increase the external pressure, what do you have to do to the vapour pressure in order to achieve boiling? (What do you have to do to the liquid to increase that vapour pressure)?

AM