HCF of three numbers

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

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✖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.ⓘ Temperature at Start of Isentropic Compression [T₁]			+10% -10%
✖Temperature at End of Isentropic Expansion is the final temperature of air at the end of an isentropic expansion process in air refrigeration systems.ⓘ Temperature at End of Isentropic Expansion [T₄]			+10% -10%
✖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.ⓘ Polytropic Index [n]			+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%
✖Ideal Temp at end of Isentropic Compression is the temperature reached at the end of an isentropic compression process in an air refrigeration system.ⓘ Ideal Temp at End of Isentropic Compression [T₂]			+10% -10%
✖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.ⓘ Ideal Temp at End of Isobaric Cooling [T₃]			+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 Temperatures, Polytropic Index and Adiabatic Index [COP_theoretical]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
COP_theoretical = (T₁-T₄)/((n/(n-1))*((γ-1)/γ)*((T₂-T₃)-(T₁-T₄)))
This formula uses 7 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.
Temperature at Start of Isentropic Compression - (Measured in Kelvin) - 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.
Temperature at End of Isentropic Expansion - (Measured in Kelvin) - Temperature at End of Isentropic Expansion is the final temperature of air at the end of an isentropic expansion process in air refrigeration systems.
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.
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.
Ideal Temp at End of Isentropic Compression - (Measured in Kelvin) - Ideal Temp at end of Isentropic Compression is the temperature reached at the end of an isentropic compression process in an air refrigeration system.
Ideal Temp at End of Isobaric Cooling - (Measured in Kelvin) - 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.

STEP 1: Convert Input(s) to Base Unit

Temperature at Start of Isentropic Compression: 300 Kelvin --> 300 Kelvin No Conversion Required
Temperature at End of Isentropic Expansion: 290 Kelvin --> 290 Kelvin No Conversion Required
Polytropic Index: 1.52 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
Ideal Temp at End of Isentropic Compression: 356.5 Kelvin --> 356.5 Kelvin No Conversion Required
Ideal Temp at End of Isobaric Cooling: 326.6 Kelvin --> 326.6 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

COP_theoretical = (T₁-T₄)/((n/(n-1))*((γ-1)/γ)*((T₂-T₃)-(T₁-T₄))) --> (300-290)/((1.52/(1.52-1))*((1.4-1)/1.4)*((356.5-326.6)-(300-290)))

Evaluating ... ...

COP_theoretical = 0.601692673895796

STEP 3: Convert Result to Output's Unit

0.601692673895796 --> No Conversion Required

FINAL ANSWER

0.601692673895796 ≈ 0.601693 <-- Theoretical Coefficient of Performance

(Calculation completed in 00.020 seconds)

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

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Created by Rushi Shah

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

Rushi Shah has created this Calculator and 25+ more calculators!

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Osmania University (OU), Hyderabad

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< Air Refrigeration Cycles Calculators

Heat Rejected during Constant pressure Cooling Process

LaTeX 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

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

Energy Performance Ratio of Heat Pump

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

Theoretical Coefficient of Performance of Refrigerator

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

< Air Refrigeration Calculators

Compression or Expansion Ratio

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

Relative Coefficient of Performance

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

Energy Performance Ratio of Heat Pump

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

Theoretical Coefficient of Performance of Refrigerator

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

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

LaTeX Go

What is Polytropic Index?

The Polytropic Index is a value that represents the relationship between pressure and volume during a thermodynamic process. It varies depending on the type of process, such as isothermal, adiabatic, or somewhere in between. In air refrigeration, this index helps determine the behavior of air during compression and expansion, affecting the efficiency and performance of the cycle. It is crucial in analyzing real-world processes where ideal conditions do not apply.

How to Calculate 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 calculator 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 calculate 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 calculate COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index using this online calculator? To use this online calculator 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. Here is how the COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index calculation can be explained with given input values -> 0.601693 = (300-290)/((1.52/(1.52-1))*((1.4-1)/1.4)*((356.5-326.6)-(300-290))).

FAQ

What is 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 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 and is represented as COP_theoretical = (T₁-T₄)/((n/(n-1))*((γ-1)/γ)*((T₂-T₃)-(T₁-T₄))) or 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))). 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, Temperature at End of Isentropic Expansion is the final temperature of air at the end of an isentropic expansion process in air refrigeration systems, 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, Heat Capacity Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume in air refrigeration systems, Ideal Temp at end of Isentropic Compression is the temperature reached at the end of an isentropic compression process in an air refrigeration system & 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.

How to calculate 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 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 is calculated using 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 calculate COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index, you need 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). With our tool, you need to enter the respective value for Temperature at Start of Isentropic Compression, Temperature at End of Isentropic Expansion, Polytropic Index, Heat Capacity Ratio, Ideal Temp at End of Isentropic Compression & Ideal Temp at End of Isobaric Cooling 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 Temperature at Start of Isentropic Compression, Temperature at End of Isentropic Expansion, Polytropic Index, Heat Capacity Ratio, Ideal Temp at End of Isentropic Compression & Ideal Temp at End of Isobaric Cooling. 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 = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)

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