How do heat engines work?

[Labminion]

I understand the general premise of a steam engine, in a very basic sense (i.e., boiler boils water, intake valve opens and steam raises piston, intake valve closes and outake valve opens, steam enters condenser as piston falls, steam condenses into liquid water). I am having trouble relating this cycle to the four steps of a Carnot heat engine (I am taking this from the Berkeley Review section on Carnot engines, paraphrased a bit):

1. Isothermal expansion of the gas. Work is done by the piston on the surroundings and heat is absorbed by the gas.

2. Adiabatic expansion of the gas (no heat is gained or lost by the system). Piston does work on the surroundings.

3. Isothermal compression of the gas. Surroundings do work on the gas; heat flows out of the engine.

4. Adiabatic compression of the gas. Surroundings do work on the gas as the piston descends, but heat is not gained or lost.

I am assuming, the above four steps relate in the following way:

1. Boiler is adding heat to the water to vaporize it at a constant temperature. The intake valve opens, and the pressure from the steam forces the piston to rise.
2. Since no heat is gained or lost in this step, is the boiler shut off? Or the intake valve closes? Not really sure how the gas will expand adiabatically while the boiler is still supplying heat.
3. Intake valve closes, outtake valve opens. Piston descends, doing work on the gas. The steam condenses into liquid. Not sure how this is isothermal? Is it because there is a heat sink in the condenser maintaining a constant cooler temperature?
4. And finally, the gas compresses adiabatically. Again, I don't see how it is adiabatic. The gas is releasing heat to condense, so where does the heat go?

Sorry if this post is long or convoluted. I keep re-reading this section in my review book but I am having a hard time comprehending it. As always, any input is very much appreciated.

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[MD Odyssey]

Sorry if this post is long or convoluted. I keep re-reading this section in my review book but I am having a hard time comprehending it. As always, any input is very much appreciated.

Honestly, the simplest way to understand heat engines is to start with a simpler system. The Carnot cycle is far more complicated than a simpler one such as the following:

Consider a gas at some original P1 and V1 (on a PV diagram, it would be the upper left hand corner):

1) Holding the pressure constant, we increase the volume reversibly by heating the gas (P1, V2). We do this by putting our container in contact with a hot reservoir. In this step, heat is transferred into the system and work is done by the gas on the surroundings.

2) Holding the volume constant, we decrease the pressure by cooling the gas (P2, V2). This is done by putting the system in contact with a cold reservoir. Heat is transferred from the system, but no work is done.

3) Holding the pressure constant, we decrease the volume by cooling the gas further (P2, V1). In this step, heat is again transferred from the system, but work is done by the surroundings on the gas.

4) Holding the volume constant, we increase the pressure by heating the gas, once again putting it in contact with a hot reservoir (P1, V1). No work is done.

The total work done by the system on the surroundings is the sum of the work done in steps 1 and 3. If you were to actually calculate this all out in terms of P1, P2, V1, and V2 you would find that the total work done will be negative. This means that the system has done work on the environment.

The basic idea behind how heat engines work is that one essentially "primes the pump" by lowering the pressure, compressing it, and then heating it and allowing it to expand. Essentially, we convert heat from the hot reservoir into the system and use that heat to do work. If the system is at equilibrium every step of the way, then the amount of work done by the system is equal to the heat transferred into the system. For a real process, this isn't the case. These two notions are what are referred to by the 2nd law of thermodynamics.

A really good lecture on heat engines is here. Check out 35:00 through to the end of the lecture. Hopefully that will help.

 

[Labminion]

Hey MD Odyssey,

Thanks for your post. Your simpler version makes sense to me. I am having difficulty overlaying those basic steps onto the step-by-step motions of a steam engine, because I don't understand which steps are adiabatic and how it is possible for them to be adiabatic if the boiler is constantly supplying heat. How is the pressure reduced in the condenser? Is the condenser kept cold somehow?

I think I am overcomplicating this.

 

[Integrated MCAT Course]

Here's a picture of a really simple steam engine. Think about how the rotational kinetic energy of the fly-wheel to understand how it keeps going through the compression stroke while the gases exhaust. It's good just to have a common sense perspective. First get to 'hey, this could work' before abstract discussions of the Carnot cycle.

A lot of folks triage the Carnot cycle in a time strained MCAT review. I believe the Carnot cycle is really important, though. One of the most important systems to understand to bridge from physics to chemistry. You may not see too many specific questions about the Carnot cycle on the MCAT, but the time you spend with with the cycle will make understanding a lot of fundamental scientific principles easier.

Here's the Carnot cycle. An isothermal expansion on Th in which Qh flows into the system followed by adiabatic expansion, which reduces temperature to Tc, followed by isothermal compression on Tc, followed by adiabatic compression, which raises temperature back up to Th.

The Carnot cycle is a great exercise for remembering how heat flow and work occur in adiabatic and isothermal transformations. Those are of great MCAT importance. Secondly, if you understand the Carnot cycle, you understand how maximum thermodynamic efficiency depends on the difference between Th and Tc.

It's key to remember that the Carnot cycle is privileged over other types of engines in being an ideal. Every step is microscopically reversible, for in the Carnot cycle, every step, even the slightest change within each step, occurs without increase in the entropy of the universe, so the Carnot cycle is just as likely to run forward as backward. It's not a practical engine. Going forward there is isothermal expansion at Th, adiabatic expansion Th -> Tc, isothermal compression at Tc, adiabatic compression Tc -> Th. Everything happens with entropy changes in the surroundings and system balanced against one another. If a steam engine could operate with Carnot efficiency, there would be no increase or decrease in entropy in the universe.

How does this lead to thermodynamic efficiency? The entropy change due to heat flow in isothermal conditions equals Q/T, and because the temperature of the system and surroundings are equal where heat flow occurs, the entropy lost or gained by the surroundings is equal to the entropy gained or lost by the system.

At Th, the entropy of the surroundings decreases by Qh/Th and the system entropy increases by that amount. At Tc, the entropy of the surroundings increases by Qc/Tc and the system entropy decreases. Qh > Qc, with the difference being the work done by the system on the surroundings. In a forward moving Carnot cycle, the system absorbs more heat at Th than it releases at Tc, so the first law tells us that net work is done by the system on the surroundings. However, and this is what leads to the second law of thermodynamics, because some heat must be expelled at Tc, the cycle shows clearly that it is impossible to convert heat into work without any other effect, so this was a practical way of stating the second law of thermodynamics.

So at a conceptual level, the Carnot cycle is the doorway from the first law of thermodynamics to the second law, if you are thinking about the macrostate, or the point of view of the benchtop and state functions, or from the kinetic theory of gases to statistical mechanics if you are thinking of the shifting microstate ensembles in physical or chemical change at the particle level. Why does it have to be this way? Why does heat flow from hot to cold, or a reaction from all A to some mixture of A and B at equilibrium? From one hot and cold to two warm spontaneously. The heat flow adds more possibilities to the cold place than removed from the hot place basically. The curve is simple describing this statistical difference, Q/T, the entropy change. Temperature equilibrium or chemical equilibrium have more possible microstate ensembles. Because equilibrium is so much more likely, being representable by so many more possible arrangements multiplicity, the chance of reverse away from equilibrium is vanishingly small. Think of how many more possible movement states are available to the gas particles filling a container than compressed in a corner by a membrane. The arrow of time is about the statistical overriding probability of disorder, so the entropy function is one for the universe that is always increasing. The Carnot cycle was the thought experiment that gave people to understand exactly how to explain the direction of change in general, as a scientific concept, in terms of a law of statistical probability, and leads to the guidance, that the entropy of the universe always increases, a principle that is never violated.

Regarding chemistry, I'm personally convinced that Gibbs developed the free energy approach to chemical equilibrium and spontaneity by contemplating the Carnot cycle as a model for chemical equilibrium. If you think about the equilibrium state of a chemical reaction as the state in which heat flows are reversible, you see that all other states are not Carnot-like. When delta G equals 0, that is another way of saying that delta H over T equals delta S, so entropy change due to heat flow into the surroundings is counterbalanced by an entropy change in the chemical system. When these are not in balance, delta G has some value, positive or negative, so there is the potential for heat flow to spontaneously occur and reaction proceeds.