Picture a world in which different engine cycles compete to be the most efficient at converting heat into work. In this world, a powerful theorem known as the Carnot theorem exists postulated by Sadi Carnot, a French engineer, which states that no cycle can surpass the efficiency of the reversible cycle(e.g. Carnot cycle, Stirling cycle etc.) that operates between the same temperature limits. That’s why the Efficiency Carnot engine is higher than any other engine that operates using an irreversible cycle(e.g.diesel cycle, otto cycle etc).
General formula for Efficiency Carnot engine
- Q1 = Heat supplied to the Carnot engine from the heat source
- Q2 = heat rejected by the Carnot engine to the sink
The relative work outputs of various piston engine cycles are given by mean effective pressure, mep or Pm which is defined as the constant pressure producing the same net work output whilst causing the piston to move through the same swept volume as in the actual cycle.
Formula for the carnot engine efficiency in terms of temperatures
- Delta T = T1 -T2
- T1 > T2
To solve problems related to the efficiency Carnot engine you need to know how it works, the different processes the Carnot engine will undergo to produce work and the T-S diagrams of a Carnot cycle.
How Carnot engine produces work?
To produce work, the Carnot engine uses heat from the source and that heat is converted into work in the engine.
Wasted heat is rejected to the sink as shown in the schematic diagram
T s diagram of a carnot cycle
In the TS diagram of a Carnot engine, the X-axis represents entropy and the Y- axis represents Temperature.
a-b and d-c represent Reversible isothermal processes and b-c and d-a represent Reversible adiabatic processes.
The area under the curve a-b-c-d represents net work output.
PV diagram of the Carnot cycle is not discussed here since the Carnot cycle efficiency depends on the Temperatures only i.e. temperatures of the source and the sink(or cooling media).
The Carnot cycle consists of the following processes
While solving problems related to the Carnot cycle it is important to know that heat transfer takes place during Isothermal processes but no heat transfer during the adiabatic processes of the Carnot cycle.
Also, note that work is done by the engine during the Isothermal heat addition (a-b) and adiabatic expansion (b-c) process.
Furthermore, work is done on the engine during the isothermal heat rejection and adiabatic compression process.
How to Improve the efficiency of a Carnot engine?
To achieve maximum efficiency in a Carnot engine, the temperature at which heat is supplied should be made as high as possible, while the temperature at which heat is rejected remains fixed. Since low temperature reservoir or sink is generally fixed by atmospheric or cooling water temperature.
COP(Efficiency) of a Carnot REfrigerating machine
Since the Carnot cycle is reversible, it can be used for refrigerating machines. Refrigerating machine’s efficiency or COP is given by the following formula.
To know more about the carnot refrigerating machine then click/tap here
Limitation of a Carnot engine
The Carnot cycle has the highest possible efficiency between any two temperatures, but it is not suitable for engines that use gaseous working fluids due to its low net work output for a given stroke volume.
To know more about the limitations of a Carnot engine then click/tap here
References
- Internal combustion engines by M.L. Mathur and R.P. Sharma
- https://en.wikipedia.org/wiki/Heat_engine
- https://byjus.com/physics/adiabatic-process/
- https://en.wikipedia.org/wiki/Isothermal_process