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

✖The temperature at Start of Isentropic Compression is the temperature from which the cycle starts.ⓘ Temperature at Start of Isentropic Compression [T₁]			+10% -10%
✖Temperature at End of Isentropic Expansion is the temperature from where isentropic expansion ends and isobaric expansion starts.ⓘ Temperature at End of Isentropic Expansion [T₄]			+10% -10%
✖The Polytropic Index is that defined via a polytropic equation of state. The index dictates the type of thermodynamic process.ⓘ Polytropic Index [n]			+10% -10%
✖The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Heat Capacity Ratio [γ]			+10% -10%
✖Ideal Temp at end of Isentropic Compression is the intermediate temperature from where isobaric cooling starts.ⓘ Ideal Temp at end of Isentropic Compression [T₂]			+10% -10%
✖Ideal Temp at end of Isobaric Cooling is the intermediate temperature in the cycle where isentropic expansion starts.ⓘ Ideal Temp at end of Isobaric Cooling [T₃]			+10% -10%

✖Theoretical Coefficient of Performance of a refrigerator is the ratio of heat Extracted from the Refrigerator to the amount of work done.ⓘ COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index [COP_theoretical]

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Formula

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

Formula

`"COP"_{"theoretical"} = ("T"_{"1"}-"T"_{"4"})/(("n"/("n"-1))*(("γ"-1)/"γ")*(("T"_{"2"}-"T"_{"3"})-("T"_{"1"}-"T"_{"4"})))`

Example

`"0.538462"=("300K"-"290K")/(("1.30"/("1.30"-1))*(("1.4"-1)/"1.4")*(("350K"-"325K")-("300K"-"290K")))`

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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 of a refrigerator is the ratio of heat Extracted from the Refrigerator to the amount of work done.
Temperature at Start of Isentropic Compression - (Measured in Kelvin) - The temperature at Start of Isentropic Compression is the temperature from which the cycle starts.
Temperature at End of Isentropic Expansion - (Measured in Kelvin) - Temperature at End of Isentropic Expansion is the temperature from where isentropic expansion ends and isobaric expansion starts.
Polytropic Index - The Polytropic Index is that defined via a polytropic equation of state. The index dictates the type of thermodynamic process.
Heat Capacity Ratio - The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Ideal Temp at end of Isentropic Compression - (Measured in Kelvin) - Ideal Temp at end of Isentropic Compression is the intermediate temperature from where isobaric cooling starts.
Ideal Temp at end of Isobaric Cooling - (Measured in Kelvin) - Ideal Temp at end of Isobaric Cooling is the intermediate temperature in the cycle where isentropic expansion starts.

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: 1.3 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
Ideal Temp at end of Isentropic Compression: 350 Kelvin --> 350 Kelvin No Conversion Required
Ideal Temp at end of Isobaric Cooling: 325 Kelvin --> 325 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)/((1.3/(1.3-1))*((1.4-1)/1.4)*((350-325)-(300-290)))

Evaluating ... ...

COP_theoretical = 0.538461538461539

STEP 3: Convert Result to Output's Unit

0.538461538461539 --> No Conversion Required

FINAL ANSWER

0.538461538461539 ≈ 0.538462 <-- 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 Temperatures, Polytropic Index and Adiabatic Index

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< 8 Air Refrigeration Cycles Calculators

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

Go 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)))

Heat Absorbed during Constant Pressure Expansion Process

Go Heat Absorbed = Specific Heat Capacity at Constant Pressure*(Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)

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)

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

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

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

< 8 Air Refrigeration Cycles Calculators

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

Heat Absorbed during Constant Pressure Expansion Process

Go Heat Absorbed = Specific Heat Capacity at Constant Pressure*(Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)

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)

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

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

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 Temperatures, Polytropic Index and Adiabatic Index Formula

What is Bell Coleman cycle?

The Bell Coleman Cycle (also called as the Joule or "reverse" Brayton cycle) is a refrigeration cycle where the working fluid is a gas that is compressed and expanded but does not change phase

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 is used to determine the value of the Coefficient of performance of the Bell-Coleman Cycle when the temperatures, polytropic index(n), and adiabatic index(γ) are given. 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 -> 0.538462 = (300-290)/((1.3/(1.3-1))*((1.4-1)/1.4)*((350-325)-(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 is used to determine the value of the Coefficient of performance of the Bell-Coleman Cycle when the temperatures, polytropic index(n), and adiabatic index(γ) are given 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))). The temperature at Start of Isentropic Compression is the temperature from which the cycle starts, Temperature at End of Isentropic Expansion is the temperature from where isentropic expansion ends and isobaric expansion starts, The Polytropic Index is that defined via a polytropic equation of state. The index dictates the type of thermodynamic process, The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume, Ideal Temp at end of Isentropic Compression is the intermediate temperature from where isobaric cooling starts & Ideal Temp at end of Isobaric Cooling is the intermediate temperature in the cycle where isentropic expansion starts.

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 is used to determine the value of the Coefficient of performance of the Bell-Coleman Cycle when the temperatures, polytropic index(n), and adiabatic index(γ) are given 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 6 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)
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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