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COP of Bell-Coleman Cycle for given Compression ratio and adiabatic index(γ) 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 2 Variables
Variables Used
Compression or Expansion Ratio- Compression or Expansion Ratio for known pressures.
Heat Capacity Ratio- The heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure (Cp) to heat capacity at constant volume (Cv). It is sometimes also known as the isentropic expansion factor and is denoted by γ (gamma) for an ideal gas.
STEP 1: Convert Input(s) to Base Unit
Compression or Expansion Ratio: 2 --> No Conversion Required
Heat Capacity Ratio: 10 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
COPtheoretical = 1/(rp^((γ-1)/γ)-1) --> 1/(2^((10-1)/10)-1)
Evaluating ... ...
COPtheoretical = 1.15464643519546
STEP 3: Convert Result to Output's Unit
1.15464643519546 --> No Conversion Required
FINAL ANSWER
1.15464643519546 <-- Theoretical Coefficient of Performance
(Calculation completed in 00.016 seconds)

11 Other formulas that you can solve using the same Inputs

COP of Bell-Coleman Cycle for given temperatures, polytropic index(n) and adiabatic index(γ)
theoretical_coefficient_of_performance = (Temperature at the start of Isentropic Compression-Temperature at the 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 the end of isobaric cooling)-(Temperature at the start of Isentropic Compression-Temperature at the end of Isentropic Expansion))) Go
Power required to maintain pressure inside the cabin(excluding ram work)
power_input = ((Mass of air*Specific Heat Capacity at Constant Pressure*Actual temperature of Rammed Air)/(Compressor efficiency))*((Cabin Pressure/Pressure of rammed air)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1) Go
Power required to maintain pressure inside the cabin(including ram work)
power_input = ((Mass of air*Specific Heat Capacity at Constant Pressure*Ambient air temperature)/(Compressor efficiency))*((Cabin Pressure/Atmospheric Pressure)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1) Go
Work done rate (isentropic condition) for adiabatic compression process when γ is given
shaft_work_isentropic = [R]*(Temperature of surface 1/((Heat Capacity Ratio-1)/Heat Capacity Ratio))*((pressure 2/pressure 1)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1) Go
Temperature ratio at the start and end of ramming process
temperature_ratio = 1+(((Velocity^2)*(Heat Capacity Ratio-1)))/(2*(Heat Capacity Ratio*[R]*Initial Temp.)) Go
Stagnation Velocity of Sound if specific heat at constant pressure is known
stagnation_velocity_of_sound = sqrt((Heat Capacity Ratio-1)*Specific Heat Capacity at Constant Pressure*Stagnation Temperature) Go
Work done in adiabatic process when Adiabatic Index is Given
work = (Mass of Gas*[R]*(Initial Temp.-Final Temp.))/(Heat Capacity Ratio-1) Go
Stagnation Velocity of Sound
stagnation_velocity_of_sound = sqrt(Heat Capacity Ratio*[R]*Stagnation Temperature) Go
Specific heat capacity at constant pressure when Adiabatic Index is Given
constant_pressure_specific_heat_capacity = (Heat Capacity Ratio*[R])/(Heat Capacity Ratio-1) Go
Stagnation Velocity of Sound if stagnation enthalpy is known
stagnation_velocity_of_sound = sqrt((Heat Capacity Ratio-1)*Stagnation enthalpy) Go
Local Sonic or Acoustic velocity at Ambient air conditions
sonic_velocity = (Heat Capacity Ratio*[R]*Initial Temp.)^0.5 Go

5 Other formulas that calculate the same Output

COP of Bell-Coleman Cycle for given temperatures, polytropic index(n) and adiabatic index(γ)
theoretical_coefficient_of_performance = (Temperature at the start of Isentropic Compression-Temperature at the 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 the end of isobaric cooling)-(Temperature at the start of Isentropic Compression-Temperature at the end of Isentropic Expansion))) Go
Coefficient of Performance (for given h4)
theoretical_coefficient_of_performance = (Enthalpy of the vapour refrigerant at T1-Enthalpy of the vapour refrigerant at T4)/(Enthalpy of the vapour refrigerant at T2-Enthalpy of the vapour refrigerant at T1) Go
Coefficient of Performance (for given hf3)
theoretical_coefficient_of_performance = (Enthalpy of the vapour refrigerant at T1-Sensible heat at temperature T3)/(Enthalpy of the vapour refrigerant at T2-Enthalpy of the vapour refrigerant at T1) Go
Theoretical Coefficient of Performance of a refrigerator
theoretical_coefficient_of_performance = Heat Extracted from Refrigerator/Work Go
Energy Performance Ratio of Heat Pump
theoretical_coefficient_of_performance = Heat Delivered to Body/Work Go

COP of Bell-Coleman Cycle for given Compression ratio and adiabatic index(γ) 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(γ)?

COP of Bell-Coleman Cycle for given Compression ratio and adiabatic index(γ) 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(γ) = 1 / (Compression ratio^((Adiabatic index -1)/Adiabatic_index) -1). Theoretical Coefficient of Performance and is denoted by COPtheoretical symbol.

How to calculate COP of Bell-Coleman Cycle for given Compression ratio and adiabatic index(γ) using this online calculator? To use this online calculator for COP of Bell-Coleman Cycle for given Compression ratio and adiabatic index(γ), enter Compression or Expansion Ratio (rp) and 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(γ) calculation can be explained with given input values -> 1.154646 = 1/(2^((10-1)/10)-1).

FAQ

What is COP of Bell-Coleman Cycle for given Compression ratio and adiabatic index(γ)?
The COP of Bell-Coleman Cycle for given Compression ratio and adiabatic index(γ) = 1 / (Compression ratio^((Adiabatic index -1)/Adiabatic_index) -1) 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 and The heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure (Cp) to heat capacity at constant volume (Cv). It is sometimes also known as the isentropic expansion factor and is denoted by γ (gamma) for an ideal gas.
How to calculate COP of Bell-Coleman Cycle for given Compression ratio and adiabatic index(γ)?
The COP of Bell-Coleman Cycle for given Compression ratio and adiabatic index(γ) = 1 / (Compression ratio^((Adiabatic index -1)/Adiabatic_index) -1) 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(γ), you need Compression or Expansion Ratio (rp) and Heat Capacity Ratio (γ). With our tool, you need to enter the respective value for Compression or Expansion Ratio and 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 and Heat Capacity Ratio. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • theoretical_coefficient_of_performance = Heat Extracted from Refrigerator/Work
  • theoretical_coefficient_of_performance = Heat Delivered to Body/Work
  • theoretical_coefficient_of_performance = (Temperature at the start of Isentropic Compression-Temperature at the 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 the end of isobaric cooling)-(Temperature at the start of Isentropic Compression-Temperature at the end of Isentropic Expansion)))
  • theoretical_coefficient_of_performance = (Enthalpy of the vapour refrigerant at T1-Enthalpy of the vapour refrigerant at T4)/(Enthalpy of the vapour refrigerant at T2-Enthalpy of the vapour refrigerant at T1)
  • theoretical_coefficient_of_performance = (Enthalpy of the vapour refrigerant at T1-Sensible heat at temperature T3)/(Enthalpy of the vapour refrigerant at T2-Enthalpy of the vapour refrigerant at T1)
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