Heat engine efficiency could approach 100%?

[Stanley514]

According to Carnot theorem, the higher temperature of a hot side and the lower temperature of a cold side the higher is the efficiency of a heat engine. Does it mean that in theory it could get anywhere close to 100%? If we take in account that 100% efficiency means it is a perpetuum mobile, does it mean that once we start to approach 100% efficiency, the demand for energy input to do some work will decrease exponentially? For example, if we have Stirling engine with 40% efficiency which requires 1 kg of a fuel to produce 1000 kW-h, then how much of the same fuel we need to produce the same work with a similar engine which is 99.99% efficient?

 

[Bandersnatch]

does it mean that once we start to approach 100% efficiency, the demand for energy input to do some work will decrease exponentially?

No, it doesn't mean that. 100% efficiency means that the engine outputs exactly as much energy as it consumes. The actual output depends on how much fuel it has consumed. It is not achieveable not because it's some exponential increase of energy consumption, but because it's impossible to eliminate all losses to friction, heating and so on.
100% efficient engine converts all the energy from fuel and outputs the same amount. For example, you put in 1 Joule of chemical energy, and it produces 1 Joule of mechanical work. 50% efficient engine reqires 2 Joules of input to get the same result.

For example, if we have Stirling engine with 40% efficiency which requires 1 kg of a fuel to produce 1000 kW-h, then how much of the same fuel we need to produce the same work with a similar engine which is 99.99% efficient?

How many times more is 99.99% than 40%?

 

[mfb]

Does it mean that in theory it could get anywhere close to 100%?

Yes, in theory.

In practice, all our cold sides are the environment, typically about at room temperature. Dumping heat into them from the engine even makes them warmer and therefore reduces the efficiency. Cooling something down to use it as colder cold side needs more energy than you can gain from it, so this approach does not help.
The typical approach to increase efficiency is going for a hotter hot side, but there you run into material issues - all materials melt, disintegrate or simply lose their strength and fall apart if they get too hot.

 

[Andrew Mason]

According to Carnot theorem, the higher temperature of a hot side and the lower temperature of a cold side the higher is the efficiency of a heat engine. Does it mean that in theory it could get anywhere close to 100%? If we take in account that 100% efficiency means it is a perpetuum mobile, does it mean that once we start to approach 100% efficiency, the demand for energy input to do some work will decrease exponentially? For example, if we have Stirling engine with 40% efficiency which requires 1 kg of a fuel to produce 1000 kW-h, then how much of the same fuel we need to produce the same work with a similar engine which is 99.99% efficient?

If the Carnot heat engine operated between a temperature arbitrarily close to absolute zero and some higher temperature, the efficiency would approach 100%. As has been pointed out, this would not violate any law of physics. It would not be a perpetual motion machine of the first or second kind.

AM

 

[Khashishi]

If 1 kg fuel produced 1000 kW-hr of work at 40% efficiency, then it would take 0.4 kg of fuel to produce 1000 kW-hr of work at 100% efficiency. There's no exponential stuff going on. It's just simple percent fractions.