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COP of Bell-Coleman Cycle for given Compression Ratio 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{1}{{r p}^{\frac{γ - 1}{γ}} - 1}

COP_theoretical - Theoretical Coefficient of Performance?r_p - Compression or Expansion Ratio?γ - Heat Capacity Ratio?

COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index Example

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

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

Here is how the COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index equation looks like.

0.6629 = \frac{1}{25^{\frac{1.4 - 1}{1.4}} - 1}

0.6629 = \frac{1}{25^{\frac{1.4 - 1}{1.4}} - 1}

0.6629 = \frac{1}{25^{\frac{1.4 - 1}{1.4}} - 1}

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Refrigeration and Air Conditioning » fx COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index

COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index Solution

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

FIRST Step Consider the formula

COP theoretical = \frac{1}{{r p}^{\frac{γ - 1}{γ}} - 1}

Next Step Substitute values of Variables

∴

COP theoretical = \frac{1}{25^{\frac{1.4 - 1}{1.4}} - 1}

Next Step Prepare to Evaluate

∴

COP theoretical = \frac{1}{25^{\frac{1.4 - 1}{1.4}} - 1}

Next Step Evaluate

∴

COP theoretical = 0.662916963873442

LAST Step Rounding Answer

∴

COP theoretical = 0.6629

COP of Bell-Coleman Cycle for given Compression Ratio 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.

Formulas to find Theoretical Coefficient of Performance

Compression or Expansion Ratio

Compression or Expansion Ratio is the ratio of the volume of air before compression or expansion to the volume after compression or expansion in air refrigeration.

Symbol: r_p

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Compression or Expansion Ratio

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.

Formulas to find Heat Capacity Ratio

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}

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

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))}

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}

Go Heat Absorbed during Constant Pressure Expansion Process

Q Absorbed = C p \cdot (T 1 - T 4)

Go Heat Rejected during Constant pressure Cooling Process

Q R = C p \cdot (T 2 - T 3)

How to Evaluate COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index?

COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index evaluator uses Theoretical Coefficient of Performance = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1) to evaluate the Theoretical Coefficient of Performance, COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index formula is defined as a theoretical coefficient of performance that evaluates the efficiency of a refrigeration system, taking into account the compression ratio and adiabatic index, providing a benchmark for optimal system design and operation. Theoretical Coefficient of Performance is denoted by COP_theoretical symbol.

How to evaluate COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index using this online evaluator? To use this online evaluator for COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index, enter Compression or Expansion Ratio (r_p) & Heat Capacity Ratio (γ) and hit the calculate button.

FAQs on COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index

What is the formula to find COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index?

The formula of COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index is expressed as Theoretical Coefficient of Performance = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1). Here is an example- 0.662917 = 1/(25^((1.4-1)/1.4)-1).

How to calculate COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index?

With Compression or Expansion Ratio (r_p) & Heat Capacity Ratio (γ) we can find COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index using the formula - Theoretical Coefficient of Performance = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1).

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=(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)))

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COP of Bell-Coleman Cycle for given Compression Ratio 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 Compression Ratio and Adiabatic Index Example

COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index Solution

COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index Formula Elements

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 Compression Ratio and Adiabatic Index?

FAQs on COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index

Variable Name

GoEnergy Performance Ratio of Heat Pump Formula

GoTheoretical Coefficient of Performance of Refrigerator Formula