The Open Door Web Site
HOME PAGE BIOLOGY CHEMISTRY PHYSICS ELECTRONICS HISTORY HISTORY of SCI & TECH MATH STUDIES LEARN FRENCH STUDY GUIDE PHOTO GALLERY
ATOMIC and NUCLEAR ELECTRICITY and MAGNETISM MEASUREMENTS MECHANICS OPTICS PRACTICAL WORK QUESTIONS RELATIVITY THERMAL PHYSICS WAVES
THERMAL PHYSICS
Google
Custom Search
The Carnot Cycle
Carnot tried to find out the maximum possible efficiency of the production of work from the internal energy of a gas.  
What follows is not the design of a practical engine.  
The cycle of operations that Carnot proposed gives the most thermodynamically efficient "engine" but not a practically useful machine.  
 
Consider a quantity of gas in a cylinder having a piston which can move without friction.
The walls of the cylinder are perfect insulators except at the base.  
An extra piece of perfect insulator is used to cover the base of the cylinder during certain parts of the cycle.  
We also have a source of energy at high temperature TH and a sink at low temperature TC  
   
We could start at any point in the cycle but, hey, why not at number 1?  
   
1. Gas in small volume, at temperature TH
   
2. Gas placed in contact with the heat source (at temperature TH)
   
3. Gas undergoes a slow isothermal expansion at TH
  Work is done by the gas during this stage
   
4. Gas removed from source and insulated
   
5. Gas undergoes adiabatic expansion until temperature reaches TC
Work is done by the gas during this stage
   
6. Gas placed in contact with heat sink (at temperature TC)
   
7. Slow isothermal compression at TC
  Work is done on the gas during this stage
   
8. Adiabatic compression until temperature reaches TH
  Work is done on the gas during this stage
   
  now back to 1 and so on and so on ...
 
 
     
p-V diagram representing the Carnot cycle
animation representing the Carnot cycle
 
 
Note that, in this cycle, the expansions are done at high temperature and the compressions are done at lower temperature  
Therefore, the work done by the gas is greater than the work done on the gas (and the difference between these quantities of work depends on the difference between the source and sink temperatures)  
Therefore, however, impractical this arrangement might be, we can still call it a heat engine  
The net effect of the cycle is that a quantity of work, w has been done and a quantity of internal energy (QC) has been transferred from a hot body (the source) to a cold body (the sink).   
Notice also that this cycle is perfectly reversible: if the sequence is followed in the reverse order the net result will be that an external agent does a quantity of work, w, transferring a quantity of internal energy, QC from the sink to the source  
   
Why do we suggest that this cycle represents the maximum possible efficiency for a heat engine?   
First, we stated that there is no friction.  
This is one way to reduce wasted energy and thus improve efficiency.    
Also, the internal energy transfers took place under conditions very close to thermal equilibrium (this is because thy took place very slowly, in a perfectly conducting container).   
   
If there is friction and/or if the energy transfers take place far from equilibrium (imagine rapid compression and expansion so the gas temporarily changes temperature) the cycle will not be reversible (in the sense defined above).   
   
After considering this cycle of operations Carnot proposed the following theorem, now called Carnotís theorem.   
The maximum efficiency of a heat engine depends on the difference in temperature between source and sink and for given source and sink temperatures the most efficient engine is a reversible engine.
 
SITE MAP
WHAT'S NEW
ABOUT
PRIVACY
COPYRIGHT
SPONSORSHIP
DONATIONS
ADVERTISING
 

© The Open Door Team
2016
Any questions or
problems regarding
this site should be
addressed to
the webmaster

© David Hoult 2017

Hosted By
Web Hosting by HostCentric

 
SiteLock
 
 
Thermal Physics Index Page