|Thermodynamics and Propulsion|
A Carnot cycle is shown in Figure 3.4. It has four processes. There are two adiabatic reversible legs and two isothermal reversible legs. We can construct a Carnot cycle with many different systems, but the concepts can be shown using a familiar working fluid, the ideal gas. The system can be regarded as a chamber enclosed by a piston and filled with this ideal gas.
The four processes in the Carnot cycle are:
The thermal efficiency of the cycle is given by the definition
In this equation, there is a sign convention implied. The quantities , as defined are the magnitudes of the heat absorbed and rejected. The quantities , on the other hand are defined with reference to heat received by the system. In this example, the former is negative and the latter is positive. The heat absorbed and rejected by the system takes place during isothermal processes and we already know what their values are from Eq. (3.1):
The efficiency can now be written in terms of the volumes at the different states as
The path from states to and from to are both adiabatic and reversible. For a reversible adiabatic process we know that . Using the ideal gas equation of state, we have . Along curve - , therefore, . Along the curve - , . Thus,
Comparing the expression for thermal efficiency Eq. (3.4) with Eq. (3.5) shows two consequences. First, the heats received and rejected are related to the temperatures of the isothermal parts of the cycle by
Second, the efficiency of a Carnot cycle is given compactly by
The efficiency can be 100% only if the temperature at which the heat is rejected is zero. The heat and work transfers to and from the system are shown schematically in Figure 3.5.
Since , looking at the - graph, does that mean the farther apart the , isotherms are, the greater efficiency? And that if they were very close, it would be very inefficient? (MP 3.2)
In the Carnot cycle, why are we only dealing with volume changes and not pressure changes on the adiabats and isotherms? (MP 3.3)
Is there a physical application for the Carnot cycle? Can we design a Carnot engine for a propulsion device? (MP 3.4)
How do we know which cycles to use as models for real processes? (MP 3.5)
Douglas Quattrochi 2006-08-06