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Isentropic Work done rate for Adiabatic Compression Process using Cp Formula

GoIsentropic Work Done Rate for Adiabatic Compression Process using Gamma Formula

GoIsentropic Work Done using Turbine Efficiency and Actual Shaft Work Formula

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

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

Isentropic Work done rate for Adiabatic Compression Process using Cp Example

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Here is how the Isentropic Work done rate for Adiabatic Compression Process using Cp equation looks like with Values.

Here is how the Isentropic Work done rate for Adiabatic Compression Process using Cp equation looks like with Units.

Here is how the Isentropic Work done rate for Adiabatic Compression Process using Cp equation looks like.

1388.6304 = 4.184 \cdot 101 \cdot ({(\frac{5200}{2500})}^{\frac{8.3145}{4.184}} - 1)

1388.6304J = 4.184J/(kg*K) \cdot 101K \cdot ({(\frac{5200Pa}{2500Pa})}^{\frac{8.3145}{4.184J/(kg*K)}} - 1)

1388.6304 = 4.184 \cdot 101 \cdot ({(\frac{5200}{2500})}^{\frac{8.3145}{4.184}} - 1)

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Isentropic Work done rate for Adiabatic Compression Process using Cp Solution

Follow our step by step solution on how to calculate Isentropic Work done rate for Adiabatic Compression Process using Cp?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

W s isentropic = 4.184J/(kg*K) \cdot 101K \cdot ({(\frac{5200Pa}{2500Pa})}^{\frac{[R]}{4.184J/(kg*K)}} - 1)

Next Step Substitute values of Constants

∴

W s isentropic = 4.184J/(kg*K) \cdot 101K \cdot ({(\frac{5200Pa}{2500Pa})}^{\frac{8.3145}{4.184J/(kg*K)}} - 1)

Next Step Prepare to Evaluate

∴

W s isentropic = 4.184 \cdot 101 \cdot ({(\frac{5200}{2500})}^{\frac{8.3145}{4.184}} - 1)

Next Step Evaluate

∴

W s isentropic = 1388.63040430223J

LAST Step Rounding Answer

∴

W s isentropic = 1388.6304J

Isentropic Work done rate for Adiabatic Compression Process using Cp 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)

Specific Heat Capacity

Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

Symbol: c

Measurement: Specific Heat CapacityUnit: J/(kg*K)

Note: Value can be positive or negative.

Formulas to find Specific Heat Capacity

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

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 Gamma

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

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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 Cp?

Isentropic Work done rate for Adiabatic Compression Process using Cp evaluator uses Shaft Work (Isentropic) = Specific Heat Capacity*Temperature of Surface 1*((Pressure 2/Pressure 1)^([R]/Specific Heat Capacity)-1) to evaluate the Shaft Work (Isentropic), The Isentropic Work done rate for Adiabatic Compression Process using Cp formula is defined as the function of temperature 1, pressure 1 and 2, and specific heat capacity at constant pressure. Shaft Work (Isentropic) is denoted by W_sisentropic symbol.

How to evaluate Isentropic Work done rate for Adiabatic Compression Process using Cp using this online evaluator? To use this online evaluator for Isentropic Work done rate for Adiabatic Compression Process using Cp, enter Specific Heat Capacity (c), Temperature of Surface 1 (T₁), Pressure 2 (P₂) & Pressure 1 (P₁) and hit the calculate button.

FAQs on Isentropic Work done rate for Adiabatic Compression Process using Cp

What is the formula to find Isentropic Work done rate for Adiabatic Compression Process using Cp?

The formula of Isentropic Work done rate for Adiabatic Compression Process using Cp is expressed as Shaft Work (Isentropic) = Specific Heat Capacity*Temperature of Surface 1*((Pressure 2/Pressure 1)^([R]/Specific Heat Capacity)-1). Here is an example- 1388.63 = 4.184*101*((5200/2500)^([R]/4.184)-1).

How to calculate Isentropic Work done rate for Adiabatic Compression Process using Cp?

With Specific Heat Capacity (c), Temperature of Surface 1 (T₁), Pressure 2 (P₂) & Pressure 1 (P₁) we can find Isentropic Work done rate for Adiabatic Compression Process using Cp using the formula - Shaft Work (Isentropic) = Specific Heat Capacity*Temperature of Surface 1*((Pressure 2/Pressure 1)^([R]/Specific Heat Capacity)-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)=[R]*(Temperature of Surface 1/((Heat Capacity Ratio-1)/Heat Capacity Ratio))*((Pressure 2/Pressure 1)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-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 Cp be negative?

Yes, the Isentropic Work done rate for Adiabatic Compression Process using Cp, measured in Energy can be negative.

Which unit is used to measure Isentropic Work done rate for Adiabatic Compression Process using Cp?

Isentropic Work done rate for Adiabatic Compression Process using Cp 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 Cp can be measured.

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Isentropic Work done rate for Adiabatic Compression Process using Cp Formula

​GoIsentropic Work Done Rate for Adiabatic Compression Process using Gamma Formula

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

Isentropic Work done rate for Adiabatic Compression Process using Cp Example

Isentropic Work done rate for Adiabatic Compression Process using Cp Solution

Isentropic Work done rate for Adiabatic Compression Process using Cp 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 Cp?

FAQs on Isentropic Work done rate for Adiabatic Compression Process using Cp

Variable Name

GoIsentropic Work Done Rate for Adiabatic Compression Process using Gamma Formula

GoIsentropic Work Done using Turbine Efficiency and Actual Shaft Work Formula