- #1
FranzDiCoccio
- 342
- 41
Hi all,
the efficiency ##\eta## of a generic heat engine working between two temperatures is bound from above by the efficiency ##\eta_{\rm C}## of a Carnot machine working between the same temperatures.
That is, if the temperatures are the same, a (ideal) Carnot machine is better than any (real) machine.
I assumed that a "Carnot refrigerator" would be also better than a regular refrigerator operating between the same temperatures. Without thinking too much I thought that the coefficient of performance ##\epsilon## of an air conditioner (AC) or heat pump (HP) would obey the same kind of inequality as the efficiency.
Upon further thinking this does not seem the case, because I find
[tex]\epsilon_{\rm AC}=\frac{1-\eta}{\eta}[/tex]
and
[tex]\epsilon_{\rm HP}=\frac{1}{\eta}[/tex]
Looking at these relations it seems that the better the heat engine, the worse the device obtained by reversing it. If the Carnot engine is the best possible machine, is the Carnot fridge the worst possible fridge?
Is this really the case, or am I getting it wrong?
Maybe it does no make sense to connect ##\eta## and ##\epsilon##, because engines and heat pumps (or air conditioners) work in different temperature ranges?
I did this because in texbooks I see many examples/exercises discussing what happens by reversing the cycle of a heat machine.
the efficiency ##\eta## of a generic heat engine working between two temperatures is bound from above by the efficiency ##\eta_{\rm C}## of a Carnot machine working between the same temperatures.
That is, if the temperatures are the same, a (ideal) Carnot machine is better than any (real) machine.
I assumed that a "Carnot refrigerator" would be also better than a regular refrigerator operating between the same temperatures. Without thinking too much I thought that the coefficient of performance ##\epsilon## of an air conditioner (AC) or heat pump (HP) would obey the same kind of inequality as the efficiency.
Upon further thinking this does not seem the case, because I find
[tex]\epsilon_{\rm AC}=\frac{1-\eta}{\eta}[/tex]
and
[tex]\epsilon_{\rm HP}=\frac{1}{\eta}[/tex]
Looking at these relations it seems that the better the heat engine, the worse the device obtained by reversing it. If the Carnot engine is the best possible machine, is the Carnot fridge the worst possible fridge?
Is this really the case, or am I getting it wrong?
Maybe it does no make sense to connect ##\eta## and ##\epsilon##, because engines and heat pumps (or air conditioners) work in different temperature ranges?
I did this because in texbooks I see many examples/exercises discussing what happens by reversing the cycle of a heat machine.