FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma Formula

GoIsentropic Work done rate for Adiabatic Compression Process using Cp Formula

GoIsentropic Work Done using Turbine Efficiency and Actual Shaft Work Formula

Fx Copy

LaTeX Copy

Shaft work (Isentropic) is work done by the shaft in a turbine/ compressor when the turbine expands reversibly and adiabatically. Check FAQs

W s isentropic = [R] \cdot (\frac{T 1}{\frac{γ - 1}{γ}}) \cdot ({(\frac{P 2}{P 1})}^{\frac{γ - 1}{γ}} - 1)

W_sisentropic - Shaft Work (Isentropic)?T₁ - Temperature of Surface 1?γ - Heat Capacity Ratio?P₂ - Pressure 2?P₁ - Pressure 1?[R] - Universal gas constant?

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma Example

With values

With units

Only example

Here is how the Isentropic Work Done Rate for Adiabatic Compression Process using Gamma equation looks like with Values.

Here is how the Isentropic Work Done Rate for Adiabatic Compression Process using Gamma equation looks like with Units.

Here is how the Isentropic Work Done Rate for Adiabatic Compression Process using Gamma equation looks like.

684.092 = 8.3145 \cdot (\frac{101}{\frac{1.4 - 1}{1.4}}) \cdot ({(\frac{5200}{2500})}^{\frac{1.4 - 1}{1.4}} - 1)

684.092J = 8.3145 \cdot (\frac{101K}{\frac{1.4 - 1}{1.4}}) \cdot ({(\frac{5200Pa}{2500Pa})}^{\frac{1.4 - 1}{1.4}} - 1)

684.092 = 8.3145 \cdot (\frac{101}{\frac{1.4 - 1}{1.4}}) \cdot ({(\frac{5200}{2500})}^{\frac{1.4 - 1}{1.4}} - 1)

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Chemical Engineering » Category

Thermodynamics » fx Isentropic Work Done Rate for Adiabatic Compression Process using Gamma

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma Solution

Follow our step by step solution on how to calculate Isentropic Work Done Rate for Adiabatic Compression Process using Gamma?

FIRST Step Consider the formula

W s isentropic = [R] \cdot (\frac{T 1}{\frac{γ - 1}{γ}}) \cdot ({(\frac{P 2}{P 1})}^{\frac{γ - 1}{γ}} - 1)

Next Step Substitute values of Variables

∴

W s isentropic = [R] \cdot (\frac{101K}{\frac{1.4 - 1}{1.4}}) \cdot ({(\frac{5200Pa}{2500Pa})}^{\frac{1.4 - 1}{1.4}} - 1)

Next Step Substitute values of Constants

∴

W s isentropic = 8.3145 \cdot (\frac{101K}{\frac{1.4 - 1}{1.4}}) \cdot ({(\frac{5200Pa}{2500Pa})}^{\frac{1.4 - 1}{1.4}} - 1)

Next Step Prepare to Evaluate

∴

W s isentropic = 8.3145 \cdot (\frac{101}{\frac{1.4 - 1}{1.4}}) \cdot ({(\frac{5200}{2500})}^{\frac{1.4 - 1}{1.4}} - 1)

Next Step Evaluate

∴

W s isentropic = 684.091976952007J

LAST Step Rounding Answer

∴

W s isentropic = 684.092J

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma Formula Elements

Variables

Constants

Shaft Work (Isentropic)

Shaft work (Isentropic) is work done by the shaft in a turbine/ compressor when the turbine expands reversibly and adiabatically.

Symbol: W_sisentropic

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Shaft Work (Isentropic)

Temperature of Surface 1

Temperature of Surface 1 is the temperature of the 1st surface.

Symbol: T₁

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature of Surface 1

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.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Heat Capacity Ratio

Pressure 2

Pressure 2 is the pressure at give point 2.

Symbol: P₂

Measurement: PressureUnit: Pa

Note: Value can be positive or negative.

Formulas to find Pressure 2

Pressure 1

Pressure 1 is the pressure at give point 1.

Symbol: P₁

Measurement: PressureUnit: Pa

Note: Value can be positive or negative.

Formulas to find Pressure 1

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

Other Formulas to find Shaft Work (Isentropic)

Go Isentropic Work done rate for Adiabatic Compression Process using Cp

W s isentropic = c \cdot T 1 \cdot ({(\frac{P 2}{P 1})}^{\frac{[R]}{c}} - 1)

Go Isentropic Work Done using Turbine Efficiency and Actual Shaft Work

W s isentropic = \frac{W s}{η T}

Go Isentropic Work Done using Compressor Efficiency and Actual Shaft Work

W s isentropic = η c \cdot W s

Other formulas in Application of Thermodynamics to Flow Processes category

Go Nozzle Efficiency

NE = \frac{ΔKE}{KE}

Go Overall Efficiency given Boiler, Cycle, Turbine, Generator, and Auxiliary Efficiency

η o = η B \cdot η C \cdot η T \cdot η G \cdot η Aux

Go Enthalpy for Pumps using Volume Expansivity for Pump

ΔH = (C pk \cdot ΔT) + (V Specific \cdot (1 - (β \cdot T)) \cdot ΔP)

Go Entropy for Pumps using Volume Expansivity for Pump

ΔS = (c \cdot \ln (\frac{T 2}{T 1})) - (β \cdot V T \cdot ΔP)

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

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma evaluator 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 evaluate 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 W_sisentropic symbol.

How to evaluate Isentropic Work Done Rate for Adiabatic Compression Process using Gamma using this online evaluator? To use this online evaluator 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.

FAQs on Isentropic Work Done Rate for Adiabatic Compression Process using Gamma

What is the formula to find Isentropic Work Done Rate for Adiabatic Compression Process using Gamma?

The formula of Isentropic Work Done Rate for Adiabatic Compression Process using Gamma is expressed as 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). Here is an example- 684.092 = [R]*(101/((1.4-1)/1.4))*((5200/2500)^((1.4-1)/1.4)-1).

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

With Temperature of Surface 1 (T₁), Heat Capacity Ratio (γ), Pressure 2 (P₂) & Pressure 1 (P₁) we can find Isentropic Work Done Rate for Adiabatic Compression Process using Gamma using the 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). This formula also uses Universal gas constant .

What are the other ways to Calculate Shaft Work (Isentropic)?

Here are the different ways to Calculate Shaft Work (Isentropic)-

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

Can the Isentropic Work Done Rate for Adiabatic Compression Process using Gamma be negative?

Yes, the Isentropic Work Done Rate for Adiabatic Compression Process using Gamma, measured in Energy can be negative.

Which unit is used to measure Isentropic Work Done Rate for Adiabatic Compression Process using Gamma?

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Isentropic Work Done Rate for Adiabatic Compression Process using Gamma can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma Formula

​GoIsentropic Work done rate for Adiabatic Compression Process using Cp Formula

​GoIsentropic Work Done using Turbine Efficiency and Actual Shaft Work Formula

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma Example

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma Solution

Isentropic Work Done Rate for Adiabatic Compression Process using Gamma Formula Elements

Other Formulas to find Shaft Work (Isentropic)

Other formulas in Application of Thermodynamics to Flow Processes category

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

FAQs on Isentropic Work Done Rate for Adiabatic Compression Process using Gamma

Variable Name

GoIsentropic Work done rate for Adiabatic Compression Process using Cp Formula

GoIsentropic Work Done using Turbine Efficiency and Actual Shaft Work Formula