Isentropic Work Done Rate for Adiabatic Compression Process using Gamma Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
Wsisentropic = [R]*(T1/((γ-1)/γ))*((P2/P1)^((γ-1)/γ)-1)
This formula uses 1 Constants, 5 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
Shaft Work (Isentropic) - (Measured in Joule) - Shaft work (Isentropic) is work done by the shaft in a turbine/ compressor when the turbine expands reversibly and adiabatically.
Temperature of Surface 1 - (Measured in Kelvin) - Temperature of Surface 1 is the temperature of the 1st surface.
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.
Pressure 2 - (Measured in Pascal) - Pressure 2 is the pressure at give point 2.
Pressure 1 - (Measured in Pascal) - Pressure 1 is the pressure at give point 1.
STEP 1: Convert Input(s) to Base Unit
Temperature of Surface 1: 101 Kelvin --> 101 Kelvin No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
Pressure 2: 5200 Pascal --> 5200 Pascal No Conversion Required
Pressure 1: 2500 Pascal --> 2500 Pascal No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Wsisentropic = [R]*(T1/((γ-1)/γ))*((P2/P1)^((γ-1)/γ)-1) --> [R]*(101/((1.4-1)/1.4))*((5200/2500)^((1.4-1)/1.4)-1)
Evaluating ... ...
Wsisentropic = 684.091976952007
STEP 3: Convert Result to Output's Unit
684.091976952007 Joule --> No Conversion Required
FINAL ANSWER
684.091976952007 684.092 Joule <-- Shaft Work (Isentropic)
(Calculation completed in 00.004 seconds)

Credits

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National Institute Of Technology (NIT), Surathkal
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23 Application of Thermodynamics to Flow Processes Calculators

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma
Go 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)
Volume Expansivity for Pumps using Entropy
Go Volume Expansivity = ((Specific Heat Capacity at Constant Pressure per K*ln(Temperature of Surface 2/Temperature of Surface 1))-Change in Entropy)/(Volume*Difference in Pressure)
Enthalpy for Pumps using Volume Expansivity for Pump
Go Change in Enthalpy = (Specific Heat Capacity at Constant Pressure per K*Overall Difference in Temperature)+(Specific Volume*(1-(Volume Expansivity*Temperature of Liquid))*Difference in Pressure)
Volume Expansivity for Pumps using Enthalpy
Go Volume Expansivity = ((((Specific Heat Capacity at Constant Pressure*Overall Difference in Temperature)-Change in Enthalpy)/(Volume*Difference in Pressure))+1)/Temperature of Liquid
Entropy for Pumps using Volume Expansivity for Pump
Go Change in Entropy = (Specific Heat Capacity*ln(Temperature of Surface 2/Temperature of Surface 1))-(Volume Expansivity*Volume*Difference in Pressure)
Isentropic Work done rate for Adiabatic Compression Process using Cp
Go Shaft Work (Isentropic) = Specific Heat Capacity*Temperature of Surface 1*((Pressure 2/Pressure 1)^([R]/Specific Heat Capacity)-1)
Overall Efficiency given Boiler, Cycle, Turbine, Generator, and Auxiliary Efficiency
Go Overall Efficiency = Boiler Efficiency*Cycle Efficiency*Turbine Efficiency*Generator Efficiency*Auxiliary Efficiency
Shaft Power
Go Shaft Power = 2*pi*Revolutions per Second*Torque Exerted on Wheel
Isentropic Change in Enthalpy using Compressor Efficiency and Actual Change in Enthalpy
Go Change in Enthalpy (Isentropic) = Compressor Efficiency*Change in Enthalpy
Compressor Efficiency using Actual and Isentropic Change in Enthalpy
Go Compressor Efficiency = Change in Enthalpy (Isentropic)/Change in Enthalpy
Actual Enthalpy Change using Isentropic Compression Efficieny
Go Change in Enthalpy = Change in Enthalpy (Isentropic)/Compressor Efficiency
Isentropic Change in Enthalpy using Turbine Efficiency and Actual Change in Enthalpy
Go Change in Enthalpy (Isentropic) = Change in Enthalpy/Turbine Efficiency
Actual Change in Enthalpy using Turbine Efficiency and Isentropic Change in Enthalpy
Go Change in Enthalpy = Turbine Efficiency*Change in Enthalpy (Isentropic)
Actual Work done using Compressor Efficiency and Isentropic Shaft Work
Go Actual Shaft Work = Shaft Work (Isentropic)/Compressor Efficiency
Isentropic Work Done using Compressor Efficiency and Actual Shaft Work
Go Shaft Work (Isentropic) = Compressor Efficiency*Actual Shaft Work
Compressor Efficiency using Actual and Isentropic Shaft Work
Go Compressor Efficiency = Shaft Work (Isentropic)/Actual Shaft Work
Actual Work Done using Turbine Efficiency and Isentropic Shaft Work
Go Actual Shaft Work = Turbine Efficiency*Shaft Work (Isentropic)
Isentropic Work Done using Turbine Efficiency and Actual Shaft Work
Go Shaft Work (Isentropic) = Actual Shaft Work/Turbine Efficiency
Turbine Efficiency using Actual and Isentropic Shaft Work
Go Turbine Efficiency = Actual Shaft Work/Shaft Work (Isentropic)
Nozzle Efficiency
Go Nozzle Efficiency = Change in Kinetic Energy/Kinetic Energy
Mass Flow Rate of Stream in Turbine (Expanders)
Go Mass Flow Rate = Work Done Rate/Change in Enthalpy
Change in Enthalpy in Turbine (Expanders)
Go Change in Enthalpy = Work Done Rate/Mass Flow Rate
Work Done Rate by Turbine (Expanders)
Go Work Done Rate = Change in Enthalpy*Mass Flow Rate

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma Formula

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)
Wsisentropic = [R]*(T1/((γ-1)/γ))*((P2/P1)^((γ-1)/γ)-1)

What is Shaft work (Isentropic)?

Shaft work (Isentropic) is work done by the shaft in a turbine/ compressor when the turbine expands reversibly and adiabatically (which is isentropic,i.e., ΔS = 0). The shaft work (isentropic) is the maximum that can be obtained from an adiabatic turbine with given inlet conditions and given discharge pressure.

How to Calculate Isentropic Work Done Rate for Adiabatic Compression Process using Gamma?

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma calculator uses 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) to calculate the Shaft Work (Isentropic), The Isentropic Work Done Rate for Adiabatic Compression Process using Gamma formula is defined as the function of temperature 1, pressure 1 and 2, and adiabatic index. Shaft Work (Isentropic) is denoted by Wsisentropic symbol.

How to calculate Isentropic Work Done Rate for Adiabatic Compression Process using Gamma using this online calculator? To use this online calculator for Isentropic Work Done Rate for Adiabatic Compression Process using Gamma, enter Temperature of Surface 1 (T1), Heat Capacity Ratio (γ), Pressure 2 (P2) & Pressure 1 (P1) and hit the calculate button. Here is how the Isentropic Work Done Rate for Adiabatic Compression Process using Gamma calculation can be explained with given input values -> 684.092 = [R]*(101/((1.4-1)/1.4))*((5200/2500)^((1.4-1)/1.4)-1) .

FAQ

What is Isentropic Work Done Rate for Adiabatic Compression Process using Gamma?
The Isentropic Work Done Rate for Adiabatic Compression Process using Gamma formula is defined as the function of temperature 1, pressure 1 and 2, and adiabatic index and is represented as Wsisentropic = [R]*(T1/((γ-1)/γ))*((P2/P1)^((γ-1)/γ)-1) or 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). Temperature of Surface 1 is the temperature of the 1st surface, 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, Pressure 2 is the pressure at give point 2 & Pressure 1 is the pressure at give point 1.
How to calculate Isentropic Work Done Rate for Adiabatic Compression Process using Gamma?
The Isentropic Work Done Rate for Adiabatic Compression Process using Gamma formula is defined as the function of temperature 1, pressure 1 and 2, and adiabatic index is calculated using 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). To calculate Isentropic Work Done Rate for Adiabatic Compression Process using Gamma, you need Temperature of Surface 1 (T1), Heat Capacity Ratio (γ), Pressure 2 (P2) & Pressure 1 (P1). With our tool, you need to enter the respective value for Temperature of Surface 1, Heat Capacity Ratio, Pressure 2 & Pressure 1 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 Shaft Work (Isentropic)?
In this formula, Shaft Work (Isentropic) uses Temperature of Surface 1, Heat Capacity Ratio, Pressure 2 & Pressure 1. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Shaft Work (Isentropic) = Specific Heat Capacity*Temperature of Surface 1*((Pressure 2/Pressure 1)^([R]/Specific Heat Capacity)-1)
  • Shaft Work (Isentropic) = Actual Shaft Work/Turbine Efficiency
  • Shaft Work (Isentropic) = Compressor Efficiency*Actual Shaft Work
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