Isentropic Work done rate for Adiabatic Compression Process using Cp Calculator

✖Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.ⓘ Specific Heat Capacity [c]			+10% -10%
✖Temperature of Surface 1 is the temperature of the 1st surface.ⓘ Temperature of Surface 1 [T₁]			+10% -10%
✖Pressure 2 is the pressure at give point 2.ⓘ Pressure 2 [P₂]			+10% -10%
✖Pressure 1 is the pressure at give point 1.ⓘ Pressure 1 [P₁]			+10% -10%

✖Shaft work (Isentropic) is work done by the shaft in a turbine/ compressor when the turbine expands reversibly and adiabatically.ⓘ Isentropic Work done rate for Adiabatic Compression Process using Cp [W_sisentropic]

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Formula

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Isentropic Work done rate for Adiabatic Compression Process using Cp

Formula

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

Example

1388.63 J = 4.184 J/(kg*K) \cdot 101 K \cdot ({(\frac{5200 Pa}{2500 Pa})}^{\frac{[R]}{4.184 J/(kg*K)}} - 1)

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Isentropic Work done rate for Adiabatic Compression Process using Cp Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shaft Work (Isentropic) = Specific Heat Capacity*Temperature of Surface 1*((Pressure 2/Pressure 1)^([R]/Specific Heat Capacity)-1)
W_sisentropic = c*T₁*((P₂/P₁)^([R]/c)-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.
Specific Heat Capacity - (Measured in Joule per Kilogram per K) - Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.
Temperature of Surface 1 - (Measured in Kelvin) - Temperature of Surface 1 is the temperature of the 1st surface.
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

Specific Heat Capacity: 4.184 Joule per Kilogram per K --> 4.184 Joule per Kilogram per K No Conversion Required
Temperature of Surface 1: 101 Kelvin --> 101 Kelvin 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

W_sisentropic = c*T₁*((P₂/P₁)^([R]/c)-1) --> 4.184*101*((5200/2500)^([R]/4.184)-1)

Evaluating ... ...

W_sisentropic = 1388.63040430223

STEP 3: Convert Result to Output's Unit

1388.63040430223 Joule --> No Conversion Required

FINAL ANSWER

1388.63040430223 ≈ 1388.63 Joule <-- Shaft Work (Isentropic)

(Calculation completed in 00.004 seconds)

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< 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)

Isentropic Work done rate for Adiabatic Compression Process using Cp

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Isentropic Work done rate for Adiabatic Compression Process using Cp Formula

Shaft Work (Isentropic) = Specific Heat Capacity*Temperature of Surface 1*((Pressure 2/Pressure 1)^([R]/Specific Heat Capacity)-1)
W_sisentropic = c*T₁*((P₂/P₁)^([R]/c)-1)

What is Thermodynamics?

Thermodynamics in physics is a branch that deals with heat, work and temperature, and their relation to energy, radiation and physical properties of matter. To be specific, it explains how thermal energy is converted to or from other forms of energy and how matter is affected by this process. Thermal energy is the energy that comes from heat. This heat is generated by the movement of tiny particles within an object, and the faster these particles move, the more heat is generated.
Thermodynamics is not concerned about how and at what rate these energy transformations are carried out. It is based on the initial and final states undergoing the change. It should also be noted that Thermodynamics is a macroscopic science. This means that it deals with the bulk system and does not deal with the molecular constitution of matter.

What is Isentropic Shaft work?

Isentropic Shaft work 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 Cp?

Isentropic Work done rate for Adiabatic Compression Process using Cp calculator uses Shaft Work (Isentropic) = Specific Heat Capacity*Temperature of Surface 1*((Pressure 2/Pressure 1)^([R]/Specific Heat Capacity)-1) to calculate 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 calculate Isentropic Work done rate for Adiabatic Compression Process using Cp using this online calculator? To use this online calculator 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. Here is how the Isentropic Work done rate for Adiabatic Compression Process using Cp calculation can be explained with given input values -> 1388.63 = 4.184*101*((5200/2500)^([R]/4.184)-1).

FAQ

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

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 and is represented as W_sisentropic = c*T₁*((P₂/P₁)^([R]/c)-1) or Shaft Work (Isentropic) = Specific Heat Capacity*Temperature of Surface 1*((Pressure 2/Pressure 1)^([R]/Specific Heat Capacity)-1). Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount, Temperature of Surface 1 is the temperature of the 1st surface, 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 Cp?

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 is calculated using Shaft Work (Isentropic) = Specific Heat Capacity*Temperature of Surface 1*((Pressure 2/Pressure 1)^([R]/Specific Heat Capacity)-1). To calculate Isentropic Work done rate for Adiabatic Compression Process using Cp, you need Specific Heat Capacity (c), Temperature of Surface 1 (T₁), Pressure 2 (P₂) & Pressure 1 (P₁). With our tool, you need to enter the respective value for Specific Heat Capacity, Temperature of Surface 1, 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 Specific Heat Capacity, Temperature of Surface 1, Pressure 2 & Pressure 1. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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