Power Required for Refrigeration System Calculator

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Air Refrigeration Systems

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✖Mass of air is both a property of air and a measure of its resistance to acceleration when a net force is applied.ⓘ Mass of Air [ma]			+10% -10%
✖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.ⓘ Specific Heat Capacity at Constant Pressure [C_p]			+10% -10%
✖Actual End Temp of Isentropic Compression is greater than the ideal temperature.ⓘ Actual End Temp of Isentropic Compression [Tt^']			+10% -10%
✖Actual temperature of Rammed Air is equal to the ideal temperature of Rammed Air.ⓘ Actual temperature of Rammed Air [T2^']			+10% -10%

✖Input Power is the power, which is required by the appliance at its input i.e., from the plug point.ⓘ Power Required for Refrigeration System [P_in]

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Formula

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Power Required for Refrigeration System

Formula

`"P"_{"in"} = ("ma"*"C"_{"p"}*("Tt"^{"'"}-"T2"^{"'"}))/60`

Example

`"9286.2kJ/min"=("120kg/min"*"1.005kJ/kg*K"*("350K"-"273K"))/60`

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Power Required for Refrigeration System Solution

STEP 0: Pre-Calculation Summary

Formula Used

Input Power = (Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))/60
P_in = (ma*C_p*(Tt^'-T2^'))/60
This formula uses 5 Variables

Variables Used

Input Power - (Measured in Watt) - Input Power is the power, which is required by the appliance at its input i.e., from the plug point.
Mass of Air - (Measured in Kilogram per Minute) - 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.
Actual End Temp of Isentropic Compression - (Measured in Kelvin) - Actual End Temp of Isentropic Compression is greater than the ideal temperature.
Actual temperature of Rammed Air - (Measured in Kelvin) - Actual temperature of Rammed Air is equal to the ideal temperature of Rammed Air.

STEP 1: Convert Input(s) to Base Unit

Mass of Air: 120 Kilogram per Minute --> 120 Kilogram per Minute No Conversion Required
Specific Heat Capacity at Constant Pressure: 1.005 Kilojoule per Kilogram per K --> 1005 Joule per Kilogram per K (Check conversion here)
Actual End Temp of Isentropic Compression: 350 Kelvin --> 350 Kelvin No Conversion Required
Actual temperature of Rammed Air: 273 Kelvin --> 273 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_in = (ma*C_p*(Tt^'-T2^'))/60 --> (120*1005*(350-273))/60

Evaluating ... ...

P_in = 154770

STEP 3: Convert Result to Output's Unit

154770 Watt -->9286.19999999998 Kilojoule per Minute (Check conversion here)

FINAL ANSWER

9286.19999999998 ≈ 9286.2 Kilojoule per Minute <-- Input Power

(Calculation completed in 00.004 seconds)

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K J Somaiya College of Engineering (K J Somaiya), Mumbai

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< 17 Air Refrigeration Systems 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 evaporative cycle

Go Actual Coefficient of Performance = (210*Tonnage of Refrigeration in TR)/(Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))

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 given exit temperature of cooling turbine

Go Mass of Air = (210*Tonnage of Refrigeration in TR)/(Specific Heat Capacity at Constant Pressure*(Temperature at End of Isentropic Expansion-Actual exit Temperature of cooling turbine))

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)

Ram Efficiency

Go Ram Efficiency = (Stagnation Pressure of System-Initial Pressure of System)/(Final Pressure of System-Initial Pressure of System)

Local Sonic or Acoustic Velocity at Ambient Air Conditions

Go Sonic Velocity = (Heat Capacity Ratio*[R]*Initial Temperature/Molecular Weight)^0.5

Initial Mass of Evaporant Required to be Carried for given Flight Time

Go Mass = (Rate of Heat Removal*Time in Minutes)/Latent Heat of Vaporization

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)

COP of Air Cycle given Input Power

Go Actual Coefficient of Performance = (210*Tonnage of Refrigeration in TR)/(Input Power*60)

Power Required for Refrigeration System Formula

Input Power = (Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))/60
P_in = (ma*C_p*(Tt^'-T2^'))/60

When is the work done in an air cycle?

Work is done on the air during the compression process, which results in an increase of the temperature and pressure of the air.

How to Calculate Power Required for Refrigeration System?

Power Required for Refrigeration System calculator uses Input Power = (Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))/60 to calculate the Input Power, The Power Required for Refrigeration System formula is defined as work done on the air during the compression per unit time. Input Power is denoted by P_in symbol.

How to calculate Power Required for Refrigeration System using this online calculator? To use this online calculator for Power Required for Refrigeration System, enter Mass of Air (ma), Specific Heat Capacity at Constant Pressure (C_p), Actual End Temp of Isentropic Compression (Tt^') & Actual temperature of Rammed Air (T2^') and hit the calculate button. Here is how the Power Required for Refrigeration System calculation can be explained with given input values -> 557.172 = (2*1005*(350-273))/60.

FAQ

What is Power Required for Refrigeration System?

The Power Required for Refrigeration System formula is defined as work done on the air during the compression per unit time and is represented as P_in = (ma*C_p*(Tt^'-T2^'))/60 or Input Power = (Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))/60. 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, Actual End Temp of Isentropic Compression is greater than the ideal temperature & Actual temperature of Rammed Air is equal to the ideal temperature of Rammed Air.

How to calculate Power Required for Refrigeration System?

The Power Required for Refrigeration System formula is defined as work done on the air during the compression per unit time is calculated using Input Power = (Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))/60. To calculate Power Required for Refrigeration System, you need Mass of Air (ma), Specific Heat Capacity at Constant Pressure (C_p), Actual End Temp of Isentropic Compression (Tt^') & Actual temperature of Rammed Air (T2^'). With our tool, you need to enter the respective value for Mass of Air, Specific Heat Capacity at Constant Pressure, Actual End Temp of Isentropic Compression & Actual temperature of Rammed Air 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 Input Power?

In this formula, Input Power uses Mass of Air, Specific Heat Capacity at Constant Pressure, Actual End Temp of Isentropic Compression & Actual temperature of Rammed Air. We can use 2 other way(s) to calculate the same, which is/are as follows -

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)
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)

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