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COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index Formula

GoEnergy Performance Ratio of Heat Pump Formula

GoTheoretical Coefficient of Performance of Refrigerator Formula

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Theoretical Coefficient of Performance is the maximum theoretical efficiency of a refrigeration system, representing the ideal performance of an air refrigeration system under ideal conditions. Check FAQs

COP theoretical = \frac{T 1 - T 4}{(\frac{n}{n - 1}) \cdot (\frac{γ - 1}{γ}) \cdot ((T 2 - T 3) - (T 1 - T 4))}

COP_theoretical - Theoretical Coefficient of Performance?T₁ - Temperature at Start of Isentropic Compression?T₄ - Temperature at End of Isentropic Expansion?n - Polytropic Index?γ - Heat Capacity Ratio?T₂ - Ideal Temp at End of Isentropic Compression?T₃ - Ideal Temp at End of Isobaric Cooling?

COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index Example

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Here is how the COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index equation looks like with Values.

Here is how the COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index equation looks like with Units.

Here is how the COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index equation looks like.

0.6017 = \frac{300 - 290}{(\frac{1.52}{1.52 - 1}) \cdot (\frac{1.4 - 1}{1.4}) \cdot ((356.5 - 326.6) - (300 - 290))}

0.6017 = \frac{300K - 290K}{(\frac{1.52}{1.52 - 1}) \cdot (\frac{1.4 - 1}{1.4}) \cdot ((356.5K - 326.6K) - (300K - 290K))}

0.6017 = \frac{300 - 290}{(\frac{1.52}{1.52 - 1}) \cdot (\frac{1.4 - 1}{1.4}) \cdot ((356.5 - 326.6) - (300 - 290))}

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Home » Engineering » Mechanical » Refrigeration and Air Conditioning » COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index

COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index Solution

Follow our step by step solution on how to calculate COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index?

FIRST Step Consider the formula

COP theoretical = \frac{T 1 - T 4}{(\frac{n}{n - 1}) \cdot (\frac{γ - 1}{γ}) \cdot ((T 2 - T 3) - (T 1 - T 4))}

Next Step Substitute values of Variables

∴

COP theoretical = \frac{300K - 290K}{(\frac{1.52}{1.52 - 1}) \cdot (\frac{1.4 - 1}{1.4}) \cdot ((356.5K - 326.6K) - (300K - 290K))}

Next Step Prepare to Evaluate

∴

COP theoretical = \frac{300 - 290}{(\frac{1.52}{1.52 - 1}) \cdot (\frac{1.4 - 1}{1.4}) \cdot ((356.5 - 326.6) - (300 - 290))}

Next Step Evaluate

∴

COP theoretical = 0.601692673895796

LAST Step Rounding Answer

∴

COP theoretical = 0.6017

COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index Formula Elements

Variables

Theoretical Coefficient of Performance

Theoretical Coefficient of Performance is the maximum theoretical efficiency of a refrigeration system, representing the ideal performance of an air refrigeration system under ideal conditions.

Symbol: COP_theoretical

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Temperature at Start of Isentropic Compression

Temperature at Start of Isentropic Compression is the initial temperature of air at the beginning of the isentropic compression process in an air refrigeration system.

Symbol: T₁

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Temperature at End of Isentropic Expansion

Temperature at End of Isentropic Expansion is the final temperature of air at the end of an isentropic expansion process in air refrigeration systems.

Symbol: T₄

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Polytropic Index

Polytropic Index is a dimensionless quantity used to describe the isentropic efficiency of a compressor in an air refrigeration system, indicating its ability to transfer heat.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Heat Capacity Ratio

Heat Capacity Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume in air refrigeration systems.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Ideal Temp at End of Isentropic Compression

Ideal Temp at end of Isentropic Compression is the temperature reached at the end of an isentropic compression process in an air refrigeration system.

Symbol: T₂

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Ideal Temp at End of Isobaric Cooling

Ideal Temp at end of Isobaric Cooling is the temperature of air at the end of the isobaric cooling process in an air refrigeration system.

Symbol: T₃

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Credits

Created by Rushi Shah

K J Somaiya College of Engineering (K J Somaiya), Mumbai

Rushi Shah has created this Formula and 25+ more formulas!

Verified by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has verified this Formula and 1200+ more formulas!

Other Formulas to find Theoretical Coefficient of Performance

Go Energy Performance Ratio of Heat Pump

COP theoretical = \frac{Q delivered}{W per min}

Go Theoretical Coefficient of Performance of Refrigerator

COP theoretical = \frac{Q ref}{w}

Other formulas in Air Refrigeration Cycles category

Go Relative Coefficient of Performance

COP relative = \frac{COP actual}{COP theoretical}

Go Compression or Expansion Ratio

r p = \frac{P 2}{P 1}

How to Evaluate COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index?

COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index evaluator uses Theoretical Coefficient of Performance = (Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)/((Polytropic Index/(Polytropic Index-1))*((Heat Capacity Ratio-1)/Heat Capacity Ratio)*((Ideal Temp at End of Isentropic Compression-Ideal Temp at End of Isobaric Cooling)-(Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion))) to evaluate the Theoretical Coefficient of Performance, COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index formula is defined as the theoretical coefficient of performance of a refrigeration system, which represents the maximum efficiency achievable by the system under ideal conditions, taking into account the temperatures, polytropic index, and adiabatic index of the system. Theoretical Coefficient of Performance is denoted by COP_theoretical symbol.

How to evaluate COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index using this online evaluator? To use this online evaluator for COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index, enter Temperature at Start of Isentropic Compression (T₁), Temperature at End of Isentropic Expansion (T₄), Polytropic Index (n), Heat Capacity Ratio (γ), Ideal Temp at End of Isentropic Compression (T₂) & Ideal Temp at End of Isobaric Cooling (T₃) and hit the calculate button.

FAQs on COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index

What is the formula to find COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index?

The formula of COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index is expressed as Theoretical Coefficient of Performance = (Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)/((Polytropic Index/(Polytropic Index-1))*((Heat Capacity Ratio-1)/Heat Capacity Ratio)*((Ideal Temp at End of Isentropic Compression-Ideal Temp at End of Isobaric Cooling)-(Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion))). Here is an example- 0.601693 = (300-290)/((1.52/(1.52-1))*((1.4-1)/1.4)*((356.5-326.6)-(300-290))).

How to calculate COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index?

With Temperature at Start of Isentropic Compression (T₁), Temperature at End of Isentropic Expansion (T₄), Polytropic Index (n), Heat Capacity Ratio (γ), Ideal Temp at End of Isentropic Compression (T₂) & Ideal Temp at End of Isobaric Cooling (T₃) we can find COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index using the formula - Theoretical Coefficient of Performance = (Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)/((Polytropic Index/(Polytropic Index-1))*((Heat Capacity Ratio-1)/Heat Capacity Ratio)*((Ideal Temp at End of Isentropic Compression-Ideal Temp at End of Isobaric Cooling)-(Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion))).

What are the other ways to Calculate Theoretical Coefficient of Performance?

Here are the different ways to Calculate Theoretical Coefficient of Performance-

Theoretical Coefficient of Performance=Heat Delivered to Hot Body/Work Done per min
Theoretical Coefficient of Performance=Heat Extracted from Refrigerator/Work Done
Theoretical Coefficient of Performance=1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)

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COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index Formula

​GoEnergy Performance Ratio of Heat Pump Formula

​GoTheoretical Coefficient of Performance of Refrigerator Formula

COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index Example

COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index Solution

COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index Formula Elements

Credits

Other Formulas to find Theoretical Coefficient of Performance

Other formulas in Air Refrigeration Cycles category

How to Evaluate COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index?

FAQs on COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index

Variable Name

GoEnergy Performance Ratio of Heat Pump Formula

GoTheoretical Coefficient of Performance of Refrigerator Formula