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

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✖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.ⓘ Compression or Expansion Ratio [r_p]			+10% -10%
✖Heat Capacity Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume in air refrigeration systems.ⓘ Heat Capacity Ratio [γ]			+10% -10%

✖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.ⓘ COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index [COP_theoretical]

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Formula

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

Formula

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

Example

0.662917 = \frac{1}{25^{\frac{1.4 - 1}{1.4}} - 1}

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

STEP 0: Pre-Calculation Summary

Formula Used

Theoretical Coefficient of Performance = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)
COP_theoretical = 1/(r_p^((γ-1)/γ)-1)
This formula uses 3 Variables

Variables Used

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Compression or Expansion Ratio: 25 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

COP_theoretical = 1/(r_p^((γ-1)/γ)-1) --> 1/(25^((1.4-1)/1.4)-1)

Evaluating ... ...

COP_theoretical = 0.662916963873442

STEP 3: Convert Result to Output's Unit

0.662916963873442 --> No Conversion Required

FINAL ANSWER

0.662916963873442 ≈ 0.662917 <-- Theoretical Coefficient of Performance

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Refrigeration and Air Conditioning » Air Refrigeration Cycles » COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index

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

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< Air Refrigeration Cycles Calculators

Heat Rejected during Constant pressure Cooling Process

Go Heat Rejected = Specific Heat Capacity at Constant Pressure*(Ideal Temp at End of Isentropic Compression-Ideal Temp at End of Isobaric Cooling)

Relative Coefficient of Performance

Go Relative Coefficient of Performance = Actual Coefficient of Performance/Theoretical Coefficient of Performance

Energy Performance Ratio of Heat Pump

Go Theoretical Coefficient of Performance = Heat Delivered to Hot Body/Work Done per min

Theoretical Coefficient of Performance of Refrigerator

Go Theoretical Coefficient of Performance = Heat Extracted from Refrigerator/Work Done

< Air Refrigeration Calculators

Compression or Expansion Ratio

Go Compression or Expansion Ratio = Pressure at End of Isentropic Compression/Pressure at Start of Isentropic Compression

Relative Coefficient of Performance

Go Relative Coefficient of Performance = Actual Coefficient of Performance/Theoretical Coefficient of Performance

Energy Performance Ratio of Heat Pump

Go Theoretical Coefficient of Performance = Heat Delivered to Hot Body/Work Done per min

Theoretical Coefficient of Performance of Refrigerator

Go Theoretical Coefficient of Performance = Heat Extracted from Refrigerator/Work Done

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

Theoretical Coefficient of Performance = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)
COP_theoretical = 1/(r_p^((γ-1)/γ)-1)

What is Bell Coleman Cycle?

The Bell Coleman Cycle, also known as the Reversed Brayton Cycle, is a refrigeration process where air is used as the refrigerant. In this cycle, air is compressed, cooled at constant pressure, expanded to lower its temperature, and then used to absorb heat from the space to be cooled. This cycle is commonly used in air refrigeration systems, especially in aviation, due to its simplicity and effectiveness in high-altitude environments.

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

COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index calculator uses Theoretical Coefficient of Performance = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1) to calculate 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 under ideal conditions, considering the compression ratio and adiabatic index of the system. Theoretical Coefficient of Performance is denoted by COP_theoretical symbol.

How to calculate COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index using this online calculator? To use this online calculator 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. Here is how the COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index calculation can be explained with given input values -> 0.662917 = 1/(25^((1.4-1)/1.4)-1).

FAQ

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

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 under ideal conditions, considering the compression ratio and adiabatic index of the system and is represented as COP_theoretical = 1/(r_p^((γ-1)/γ)-1) or Theoretical Coefficient of Performance = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1). 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 & Heat Capacity Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume in air refrigeration systems.

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

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 under ideal conditions, considering the compression ratio and adiabatic index of the system is calculated using Theoretical Coefficient of Performance = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1). To calculate COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index, you need Compression or Expansion Ratio (r_p) & Heat Capacity Ratio (γ). With our tool, you need to enter the respective value for Compression or Expansion Ratio & Heat Capacity Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Theoretical Coefficient of Performance?

In this formula, Theoretical Coefficient of Performance uses Compression or Expansion Ratio & Heat Capacity Ratio. We can use 3 other way(s) to calculate the same, which is/are as follows -

Theoretical Coefficient of Performance = Heat Extracted from Refrigerator/Work Done
Theoretical Coefficient of Performance = Heat Delivered to Hot Body/Work Done per min
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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