heat engine and carnot cycle

1. Heat Engines and The Carnot
Cycle

2. First Statement of the Second Law of Thermodynamics
The first statement of the second law is a statement from
common experience.
1. When two objects, one hot and the other cold, come
into contact, heat energy will be transferred from the
system at higher temperature to the system at lower
temperature, but not vice versa.
2. The 1st law of thermodynamics does not clarify this,
that is why we have the 2nd Law

3. Second Statement of the Second Law: Heat Engines
A heat engine is a device that is capable of changing
thermal energy (QH), also known as the input heat or
heat of combustion of the fuel, into useful work (W).

4. Heat Engines
• The diagram shows that heat QH flows from the high
temp reservoir and part fo the heat is transformed to
work and part of the thermal energy is discarded as heat
QL to a low temperature reservoir (large area of constant
temperature)
Simplified Heat Engine Process

5. Heat engines cannot be made to be 100% efficient
and while part of the heat energy is converted to
useful work, the remaining heat energy will be
rejected to the environment or surroundings as
waste heat (Qc) like the exhaust from a car
engine for example. Therefore,
W = QH - Qc

6. Efficiency of Engines
• e - efficiency
• e = W/QH x 100
• or e = 1- QL/QH

8. Example I
• An internal combustion engine operates
with an efficiency of 18%. The engine
produces 2100W of power, on average,
while operating at peak performance. A)
What is the rate of energy flow from the
high temperature reservoir to the engine?
B) What is the rate of energy flow from the
engine to the low temperature reservoir?

9. Answer
• 12000J/s, 9900J/s

10. Carnot Cycle
• Sadi Carnot (1824) published that the
maximum efficiency for a heat engine
depends on the ratio of the absolute
operating temperature TH and TL.

11. CARNOT ENGINE
Carnot imagined the “ideal engine” known as a Carnot
engine, energy losses due to internal friction or
turbulence present in the fuel after ignition, etc. are not
considered.
The most efficient heat engine cycle is the Carnot cycle,
consisting of two isothermals and two adiabatic
processes. All 4 processes are said to be reversible or
in equilibrium states.

13. Carnot Explained
• The Carnot cycle can be thought of as the most
efficient heat engine cycle allowed by physical
laws. When the second law of thermodynamics
states that not all the supplied heat in a heat
engine can be used to do work, the Carnot
efficiency sets the limiting value on the fraction
of the heat which can be so used.

14. Carnot Efficiency
• e = W/QH
– Can be rewritten as
• e = (QH – Qc)/QH
• Only Valid for Ideal Engines
• Tc/TH = Qc/QH

15. Carnot determined that
the maximum efficiency
(e) that could be realized
from a heat engine
depends on the
temperature of the input
heat (TH) and the exhaust
heat (TC) where TH and TC
are expressed in Kelvin.

16. Carnot Explained
• By comparing the work done by the gas in the first two
processes to the work done on the gas in the final two
processes we see that the difference in the area
bounded by the cycle 1,2,3,4.
• The gas moved through a complete cycle, so the net
change in internal energy is zero
• ΔU = 0

17. The maximum efficiency (e) or Carnot efficiency of a
heat engine is determined by:
Using the input and waste heat
temperatures:
e = (QH – QL)/QH
e = (TH – Tc)/TH
Is it possible to be mathematically 100% efficient???????

18. Carnot Impossibility
• If e = 100%
– Then ΔU = 0
• If ΔU = 0 then ΔS = 0
• Why is it impossible for ΔS = 0

19. Carnot Impossibility
• ΔS = 0 only occurs at absolute zero which
is impossible to achieve.
• No device can transform a given amount
of heat energy into work.
– Automobiles have efficiencies in the 20 to
35%.

20. Example II
• What is the maximum efficiency possible
of an engine that operates between 500°C
and 250°C?

21. Answer
• 32%

22. Example III
• The exhaust temperature of a heat engine
is 240°C. The engine produces 500J of
work and has a Carnot efficiency of 45%.
A) What is the temperature of the heat
source? B) What heat is extracted from
the heat source? C) What heat is
delivered to the cold reservoir?

23. Answer
• 930K, 1100J, 610J