Mass of air to produce Q tonnes of refrigeration Calculator

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✖The Tonnage of Refrigeration in TR is defined as the rate of heat transfer that results in the freezing or melting of 1 short ton of pure ice at 0 °C in 24 hours.ⓘ Tonnage of Refrigeration in TR [Q]			+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%
✖Inside temperature of cabin is the temperature inside the aircraft due to the occupancy and heating equipments.ⓘ Inside temperature of cabin [T₆]			+10% -10%
✖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.ⓘ Actual temperature at end of isentropic expansion [T5^']			+10% -10%

✖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 to produce Q tonnes of refrigeration [ma]

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Formula

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Mass of air to produce Q tonnes of refrigeration

Formula

`"ma" = (210*"Q")/("C"_{"p"}*("T"_{"6"}-"T5"^{"'"}))`

Example

`"7.522388kg/min"=(210*"3")/("1.005kJ/kg*K"*("270K"-"265K"))`

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Mass of air to produce Q tonnes of refrigeration Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
ma = (210*Q)/(C_p*(T₆-T5^'))
This formula uses 5 Variables

Variables Used

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.
Tonnage of Refrigeration in TR - The Tonnage of Refrigeration in TR is defined as the rate of heat transfer that results in the freezing or melting of 1 short ton of pure ice at 0 °C in 24 hours.
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.
Inside temperature of cabin - (Measured in Kelvin) - Inside temperature of cabin is the temperature inside the aircraft due to the occupancy and heating equipments.
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

Tonnage of Refrigeration in TR: 3 --> 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)
Inside temperature of cabin: 270 Kelvin --> 270 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

ma = (210*Q)/(C_p*(T₆-T5^')) --> (210*3)/(1005*(270-265))

Evaluating ... ...

ma = 0.125373134328358

STEP 3: Convert Result to Output's Unit

0.125373134328358 Kilogram per Second -->7.52238805970149 Kilogram per Minute (Check conversion here)

FINAL ANSWER

7.52238805970149 ≈ 7.522388 Kilogram per Minute <-- Mass of Air

(Calculation completed in 00.004 seconds)

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Credits

Created by Rushi Shah

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

Rushi Shah has created this Calculator and 25+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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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)

Mass of air to produce Q tonnes of refrigeration Formula

How does simple air cycle work?

Air cycle refrigeration works on the reverse Brayton or Joule cycle. Air is compressed and then heat removed, this air is then expanded to a lower temperature than before it was compressed.

How to Calculate Mass of air to produce Q tonnes of refrigeration?

Mass of air to produce Q tonnes of refrigeration calculator uses 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)) to calculate the Mass of Air, The Mass of air to produce Q tonnes of refrigeration formula is defined as both a property of air and a measure of its resistance to acceleration when a net force is applied. Mass of Air is denoted by ma symbol.

How to calculate Mass of air to produce Q tonnes of refrigeration using this online calculator? To use this online calculator for Mass of air to produce Q tonnes of refrigeration, enter Tonnage of Refrigeration in TR (Q), Specific Heat Capacity at Constant Pressure (C_p), Inside temperature of cabin (T₆) & Actual temperature at end of isentropic expansion (T5^') and hit the calculate button. Here is how the Mass of air to produce Q tonnes of refrigeration calculation can be explained with given input values -> 451.3433 = (210*3)/(1005*(270-265)).

FAQ

What is Mass of air to produce Q tonnes of refrigeration?

The Mass of air to produce Q tonnes of refrigeration formula is defined as both a property of air and a measure of its resistance to acceleration when a net force is applied and is represented as ma = (210*Q)/(C_p*(T₆-T5^')) or 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)). The Tonnage of Refrigeration in TR is defined as the rate of heat transfer that results in the freezing or melting of 1 short ton of pure ice at 0 °C in 24 hours, 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, Inside temperature of cabin is the temperature inside the aircraft due to the occupancy and heating equipments & 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 Mass of air to produce Q tonnes of refrigeration?

The Mass of air to produce Q tonnes of refrigeration formula is defined as both a property of air and a measure of its resistance to acceleration when a net force is applied is calculated using 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)). To calculate Mass of air to produce Q tonnes of refrigeration, you need Tonnage of Refrigeration in TR (Q), Specific Heat Capacity at Constant Pressure (C_p), Inside temperature of cabin (T₆) & Actual temperature at end of isentropic expansion (T5^'). With our tool, you need to enter the respective value for Tonnage of Refrigeration in TR, Specific Heat Capacity at Constant Pressure, Inside temperature of cabin & 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 Mass of Air?

In this formula, Mass of Air uses Tonnage of Refrigeration in TR, Specific Heat Capacity at Constant Pressure, Inside temperature of cabin & Actual temperature at end of isentropic expansion. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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