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)
COPtheoretical = 1/(rp^((γ-1)/γ)-1)
This formula uses 3 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.
Compression or Expansion Ratio - Compression or Expansion Ratio for known pressures.
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.
STEP 1: Convert Input(s) to Base Unit
Compression or Expansion Ratio: 2 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
COPtheoretical = 1/(rp^((γ-1)/γ)-1) --> 1/(2^((1.4-1)/1.4)-1)
Evaluating ... ...
COPtheoretical = 4.56592536950404
STEP 3: Convert Result to Output's Unit
4.56592536950404 --> No Conversion Required
FINAL ANSWER
4.56592536950404 4.565925 <-- Theoretical Coefficient of Performance
(Calculation completed in 00.004 seconds)

Credits

Created by Rushi Shah
K J Somaiya College of Engineering (K J Somaiya), Mumbai
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5 Bell-Coleman Cycle or Reversed Brayton or Joule Cycle 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

5 Bell-Coleman Cycle or Reversed Brayton or Joule Cycle 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

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)
COPtheoretical = 1/(rp^((γ-1)/γ)-1)

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 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, The COP of Bell-Coleman Cycle for given Compression ratio and adiabatic index is a performance rating that tells us how effective a heat pump or air conditioner is at transferring heat versus the amount of electrical power it consumes. Theoretical Coefficient of Performance is denoted by COPtheoretical 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 (rp) & 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 -> 4.565925 = 1/(2^((1.4-1)/1.4)-1).

FAQ

What is COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index?
The COP of Bell-Coleman Cycle for given Compression ratio and adiabatic index is a performance rating that tells us how effective a heat pump or air conditioner is at transferring heat versus the amount of electrical power it consumes and is represented as COPtheoretical = 1/(rp^((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 for known pressures & 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.
How to calculate COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index?
The COP of Bell-Coleman Cycle for given Compression ratio and adiabatic index is a performance rating that tells us how effective a heat pump or air conditioner is at transferring heat versus the amount of electrical power it consumes 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 (rp) & 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 2 other way(s) to calculate the same, which is/are as follows -
  • 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)))
  • 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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