# Is 'stacking' engines a viable way to maximize efficiency?

Suppose we have $$n$$ carnot engines connected together labelled as $$C_1,C_2...C_n$$, now suppose we feed an energy of $$E_1$$ into $$C_1$$, now by the second law of thermodynamics, it must be that efficiency can't be $$1$$ , so some heat is dumped to environment, let's say we 'direct' the heat dump $$E_2$$ into $$C_2$$, and we keep doing this procedure till we reach the $$n-1th$$ engine. Now, the heat dump of this engine into n+1th engine must be very small in magnitude ( say we have enough engines such that this happens), then this if we look at the at the total efficiency of the process:

$$e= \frac{Q_{in-sys} - Q_{out-sys} }{Q_{in-sys} }$$

The question I have is how to achieve the step where we direct the heat loss from the $$ith$$ engine to the $$i+1th$$ engine. If there was a way to do that I Think this would be a viable method for maximizing heat engnine output.

• Ist law: energy can be changed from one form to another, @nd Law you never get all of it. So the more engines means more losses. Commented Mar 19, 2021 at 16:22
• How so ? The i+1th engine runs of the loss of ith engine
– user28616
Commented Mar 19, 2021 at 16:24
• Thats where entropy comes in. Commented Mar 19, 2021 at 16:38
• Because you won't catch all the losses... Commented Mar 19, 2021 at 16:38

I will try to expand on Tiger guys answer, and more specifically on the example for the exhaust of a gas turbine.

A typical gas turbine has a maximum temperature of about $$1000^oC$$ and assuming that the output gases are at 500[C], so in theory you could get a maximum efficiency of $$e_1= 1- \frac{500+273}{1000+273}=60%$$

So there would have been about 40% energy available to recover.

Now the thing is that if the second engine goes from 500 to 23$$[^oC]$$, then

$$e_2= 1- \frac{23+273}{500+273}=38%$$

So in total you would have gained, 60% from the original energy and 0.38*0.4=15.2% from the second engine. So a total of about 75%.

Now the thing is that if you were to have a single engine starting from 1000 and ending at 23, you would theoretically get a maximum efficiency of 76.75%.

So multiple engines, don't necessarily have a better efficiency.

Of course, reality comes into play, and the maximum efficiency of about 70% in the above gas turbine example, is in real life less than 40% at best, even at the most carefully engineered and designed machines (due to losses and other not recoverable energy).

• So, is it correct to think that lower efficiency of engine (more heat losss) , the more effective the idea I had is or is it worse? (from your irl example)
– user28616
Commented Mar 19, 2021 at 18:06
• I am not clear on what you are asking. Could you rephrase it? Commented Mar 19, 2021 at 18:16
• So, you gave the example that irl engines have only 40% efficiency , this would mean that 60% is lost , so there is more heat for a second engine to capture. This makes it seem like at lower efficiency of an engine, stacking engine is a good idea, is that right?
– user28616
Commented Mar 19, 2021 at 18:17
• @NMech well good answer, but looks like it was sadly wasted... Commented Mar 19, 2021 at 20:05
• It's worth noting that putting two engines in series is done all the time in Combined Cycle Gas Turbine power plants. The first engine is a gas turbine where the fuel is burned to power a turbine. The exhaust goes through a boiler to generate steam, which powers another turbine.
– Mark
Commented Mar 19, 2021 at 20:06

Capturing waste heat is a very viable way to increase the efficiency of a system, but it isn't a panacea.

Real world limits come into play. The 2nd Law says you'll never be able to capture all the waste heat, and as the heat loss gets less (and thus the temperature of the waste heat), the lower the efficiency of the machine that captures it.

There are lots of ways, for example, to capture exhaust heat of a gas turbine. But then capturing the waste heat from that process quickly becomes impractical. This might work as a thought experiment, but like trying to use a Stirling engine in the real world, barriers show up quickly.

I'd say it's a fairly common exploit to squeeze what extra you can out of your heat source. The Titanic had stacked engines. The center shaft was driven by a blow-down turbine fed from the exhausts from the port and starboard engines.