Expansion Work Solution

STEP 0: Pre-Calculation Summary
Formula Used
Work Done per min = Mass of Air*Specific Heat Capacity at Constant Pressure*(Temperature at the end of cooling process-Actual temperature at end of isentropic expansion)
Wper min = ma*Cp*(T4-T5')
This formula uses 5 Variables
Variables Used
Work Done per min - (Measured in Watt) - Work Done per min is when a force that is applied to an object moves that object.
Mass of Air - (Measured in Kilogram per Second) - Mass of air is both a property of air and a measure of its resistance to acceleration when a net force is applied.
Specific Heat Capacity at Constant Pressure - (Measured in Joule per Kilogram per K) - Specific Heat Capacity at Constant Pressure means the amount of heat that is required to raise the temperature of a unit mass of gas by 1 degree at constant pressure.
Temperature at the end of cooling process - (Measured in Kelvin) - Temperature at the end of cooling process is also the temperature at which isentropic expansion starts.
Actual temperature at end of isentropic expansion - (Measured in Kelvin) - Actual temperature at end of isentropic expansion is the exit temperature of the cooling turbine and is the temperature at which the refrigeration process starts.
STEP 1: Convert Input(s) to Base Unit
Mass of Air: 120 Kilogram per Minute --> 2 Kilogram per Second (Check conversion here)
Specific Heat Capacity at Constant Pressure: 1.005 Kilojoule per Kilogram per K --> 1005 Joule per Kilogram per K (Check conversion here)
Temperature at the end of cooling process: 385 Kelvin --> 385 Kelvin No Conversion Required
Actual temperature at end of isentropic expansion: 265 Kelvin --> 265 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Wper min = ma*Cp*(T4-T5') --> 2*1005*(385-265)
Evaluating ... ...
Wper min = 241200
STEP 3: Convert Result to Output's Unit
241200 Watt -->14472 Kilojoule per Minute (Check conversion here)
FINAL ANSWER
14472 Kilojoule per Minute <-- Work Done per min
(Calculation completed in 00.004 seconds)

Credits

Created by Rushi Shah
K J Somaiya College of Engineering (K J Somaiya), Mumbai
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11 Simple Air Cooling System Calculators

Power required to maintain pressure inside cabin excluding ram work
Go Input Power = ((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)
Power Required to Maintain Pressure inside Cabin including Ram Work
Go Input Power = ((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)
C.O.P. of simple air cycle
Go Actual Coefficient of Performance = (Inside temperature of cabin-Actual temperature at end of isentropic expansion)/(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air)
Mass of air to produce Q tonnes of refrigeration
Go Mass of Air = (210*Tonnage of Refrigeration in TR)/(Specific Heat Capacity at Constant Pressure*(Inside temperature of cabin-Actual temperature at end of isentropic expansion))
Expansion Work
Go Work Done per min = Mass of Air*Specific Heat Capacity at Constant Pressure*(Temperature at the end of cooling process-Actual temperature at end of isentropic expansion)
Refrigeration Effect Produced
Go Refrigeration Effect Produced = Mass of Air*Specific Heat Capacity at Constant Pressure*(Inside temperature of cabin-Actual temperature at end of isentropic expansion)
Heat rejected during cooling process
Go Heat Rejected = Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Temperature at the end of cooling process)
Compression Work
Go Work Done per min = Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air)
Power Required for Refrigeration System
Go Input Power = (Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))/60
Temperature Ratio at Start and End of Ramming Process
Go Temperature Ratio = 1+(Velocity^2*(Heat Capacity Ratio-1))/(2*Heat Capacity Ratio*[R]*Initial Temperature)
COP of Air Cycle for given Input Power and Tonnage of Refrigeration
Go Actual Coefficient of Performance = (210*Tonnage of Refrigeration in TR)/(Input Power*60)

Expansion Work Formula

Work Done per min = Mass of Air*Specific Heat Capacity at Constant Pressure*(Temperature at the end of cooling process-Actual temperature at end of isentropic expansion)
Wper min = ma*Cp*(T4-T5')

How does an expansion turbine work?

The expander principle relies on converting kinetic energy to useful energy / electricity by using turbines and electrical generators. As the gas flows from the high pressure stream into the turbo-expander, the gas spins the turbine, which is coupled to a generator that produces electricity.

How to Calculate Expansion Work?

Expansion Work calculator uses Work Done per min = Mass of Air*Specific Heat Capacity at Constant Pressure*(Temperature at the end of cooling process-Actual temperature at end of isentropic expansion) to calculate the Work Done per min, The Expansion Work formula is defined as the product of the mass of air, constant pressure specific heat capacity, and difference of actual temperature at the end of the isentropic expansion and cooling process. Work Done per min is denoted by Wper min symbol.

How to calculate Expansion Work using this online calculator? To use this online calculator for Expansion Work, enter Mass of Air (ma), Specific Heat Capacity at Constant Pressure (Cp), Temperature at the end of cooling process (T4) & Actual temperature at end of isentropic expansion (T5') and hit the calculate button. Here is how the Expansion Work calculation can be explained with given input values -> 868.32 = 2*1005*(385-265).

FAQ

What is Expansion Work?
The Expansion Work formula is defined as the product of the mass of air, constant pressure specific heat capacity, and difference of actual temperature at the end of the isentropic expansion and cooling process and is represented as Wper min = ma*Cp*(T4-T5') or Work Done per min = Mass of Air*Specific Heat Capacity at Constant Pressure*(Temperature at the end of cooling process-Actual temperature at end of isentropic expansion). Mass of air is both a property of air and a measure of its resistance to acceleration when a net force is applied, Specific Heat Capacity at Constant Pressure means the amount of heat that is required to raise the temperature of a unit mass of gas by 1 degree at constant pressure, Temperature at the end of cooling process is also the temperature at which isentropic expansion starts & Actual temperature at end of isentropic expansion is the exit temperature of the cooling turbine and is the temperature at which the refrigeration process starts.
How to calculate Expansion Work?
The Expansion Work formula is defined as the product of the mass of air, constant pressure specific heat capacity, and difference of actual temperature at the end of the isentropic expansion and cooling process is calculated using Work Done per min = Mass of Air*Specific Heat Capacity at Constant Pressure*(Temperature at the end of cooling process-Actual temperature at end of isentropic expansion). To calculate Expansion Work, you need Mass of Air (ma), Specific Heat Capacity at Constant Pressure (Cp), Temperature at the end of cooling process (T4) & Actual temperature at end of isentropic expansion (T5'). With our tool, you need to enter the respective value for Mass of Air, Specific Heat Capacity at Constant Pressure, Temperature at the end of cooling process & Actual temperature at end of isentropic expansion 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 Work Done per min?
In this formula, Work Done per min uses Mass of Air, Specific Heat Capacity at Constant Pressure, Temperature at the end of cooling process & Actual temperature at end of isentropic expansion. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Work Done per min = Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air)
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