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There are many different power cycles. This article will give a comprehensive overview of the Carnot and Otto Cycle and present different equations for considering these power cycles.
These cycles describe how energy is transformed from one form to another, often to generate mechanical work or electricity. The Carnot cycle involves two isothermal and two adiabatic processes, illustrating reversible and idealised heat transfer. Whereas the Otto Cycle describes the operation of spark-ignition engines.

Check out our Power Cycle calculators to run these calcs:
  1. Carnot Cycle
  2. Otto Cycle

Definitions

Here are some important definitions to keep in mind for Carnot cycles!

  1. Isobaric: the process takes place under constant pressure.
  2. Adiabatic: no heat is transferred, and change in internal energy is only the result of work.
  3. Isothermal: the process takes place under constant temperature.
  4. Internal Energy: the total kinetic energy in a system due to the motion of molecules and the potential energy in atoms.
  1. Isentropic: an ideal thermodynamic process that is both adiabatic (no heat transfer) and reversible, there is constant entropy.
  2. Compression: a reduction in volume.
  3. Addition: i.e. an isobaric addition, where heat may increase and be added under constant pressure.
  4. Rejection: with respect to thermodynamics, a rejection usually involves the release of heat to the surroundings during a process.

Carnot Cycle

French engineer Sadi Carnot created the Carnot cycle in the early 19th century. It is a theoretical construct representing the most efficient heat engine possible. The Carnot cycle is characterised by two isothermal and two adiabatic processes, highlighting the significance of reversible and ideal heat transfer.
Figure 1: Temperature vs Entropy Graph for a Carnot Cycle

Figure 2: Diagram of a Carnot Cycle


1-2 SE Isentropic Expansion
3-4 SC Isentropic Compression
2-3 TR Isothermal Heat Rejection
4-1 TA Isothermal Heat Addition

The following are the variables for the equations

  1. η = efficiency, i.e. efficiency of a Carnot cycle.
  2. Q(A) = heat transferred from the hot reservoir.
  1. Q(R) = heat transferred from the cold reservoir.
  2. ΔS = the change in entropy from the hot reservoir to the cold reservoir.
  3. T(H) = temperature at the hot reservoir.
  1. T(L) = temperature at the cold reservoir.
  1. W = work done by the system, the net heat absorbed.

QA=THΔSQ_A=T_H{\Delta}S
Q(A) is heat transferred from the hot reservoir to the system per cycle, where T(H) is the temperature of the hot reservoir and ΔS is the change in entropy.

QR=TLΔSQ_R=T_L{\Delta}S
Q(R) is heat transferred from the cold reservoir to the system per cycle, where T(L) is the temperature of the cold reservoir and ΔS is the change in entropy.

Wnet=QA−QRW_{net}=Q_A-Q_R
The work done by the system is the difference between the thermal energy at the hot reservoir and the cold reservoir.

η=1−TLTH\eta=1-\frac{T_L}{T_H}
This equation calculates the efficiency of a Carnot Cycle.
Carnot Cycle efficiency can be increased by increasing T(H) and lowering T(L).

Use this calculator to solve these equations!

Carnot Cycle Calculator

Otto Cycle

The Otto cycle is named after its inventor Nikolaus Otto. The Otto Cycle is the basis for internal combustion engines used in most automobiles. Unlike the Diesel Cycle, which works under constant pressure, the Otto Cycle works under constant volume. This cycle has four distinct phases:
  1. Intake
  2. Compression
  3. Power
  4. Exhaust
It describes the operation of spark-ignition engines, where air-fuel mixtures are compressed and ignited by a spark plug, providing power to propel vehicles.
Figure 3: Pressure vs Volume Graph for an Otto Cycle

Figure 4: Diagram of an Otto Cycle

1-2 SC Isentropic Compression
2-3 VA Isometric Addition
3-4 SE Isentropic Expansion
4-1 VR Isometric Rejection

The following are the variables for the equations


rk, equation 1=V1V2r_{k,\ equation\ 1}=\frac{V_1}{V_2}

rk, equation 2=1+%c%cr_{k,\ equation\ 2}=\frac{1+\%c}{\%c}
r(k), the compression ratio, is the ratio of the volume at the first state to the volume at the second state.

re=V4V3r_e=\frac{V_4}{V_3}
r(e), the expansion ratio, is the ratio of the volume at the fourth state to the volume at the third state.

c=V2V0c=\frac{V_2}{V_0}

rk, equation 3=rer_{k,\ equation\ 3}=r_e
In an ideal Otto cycle the compression ratio is the same as the expansion ratio.

η=1−1rkk−1\eta=1-\frac{1}{r_k^{k-1}}
The efficiency of the cycle is a function of the compression ratio.


MEP=[(rp−1)(rkk−1)](k−1)(1−1rk)MEP=\frac{[(r_p-1)(rk^{k-1})]}{(k-1)(1-\frac{1}{rk})}
The mean effective pressure is the average pressure in an internal combustion engine over the entire engine cycle.

Use this calculator to solve these equations!

Otto Cycle Calculator

Power cycles are foundational concepts in thermodynamics and engineering, serving as the fundamental frameworks for various energy conversion systems.
The Carnot and Otto cycles are two important concepts in thermodynamics and engineering, each playing an integral role in understanding energy conversion processes and the operation of various heat engines.


Additional Resources

If you liked this, check out our other articles and resources!
  1. Check out our library of templates here.
  1. Diesel Cycle
  2. Duel Combustion Cycle
  3. Brayton Cycles
  4. Introduction to Thermodynamics
  5. Importance of Mechanical Engineering Calculation Templates

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References

  1. LinkedIn. 2023. Important Thermodynamic Concepts. [ONLINE] Available at: https://www.linkedin.com/feed/update/urn:li:activity:7095576421120548864?utm_source=share&utm_medium=member_desktop. [Accessed 24 October 2023].
  2. Physics Stack Exchange. 2023. Apparent contradiction concerning the net work of a Carnot cycle. [ONLINE] Available at: https://physics.stackexchange.com/questions/524480/apparent-contradiction-concerning-the-net-work-of-a-carnot-cycle. [Accessed 26 October 2023].
  3. slideshare.net. 2014. Power cycles 1 | PPT - SlideShare. [ONLINE] Available at: https://www.slideshare.net/nssen/power-cycles-1. [Accessed 31 October 2023].
  4. Testbook. 2022. Otto Cycle. [ONLINE] Available at: https://testbook.com/question-answer/thermal-efficiency-of-otto-cycle-can-be-represente--5e7b33f2f60d5d29f99c6b62. [Accessed 30 October 2023].
  5. Wikipedia. 2023. Carnot cycle. [ONLINE] Available at: https://en.wikipedia.org/wiki/Carnot_cycle. [Accessed 30 October 2023].
  6. Wikipedia. 2023. Entropy. [ONLINE] Available at: https://en.wikipedia.org/wiki/Entropy. [Accessed 30 October 2023].