Discharge Temperature at High pressure compressor when Cooling ratio is constant Solution

STEP 0: Pre-Calculation Summary
Formula Used
Discharge Temperature at high pressure compressor = Suction Pressure of Low Pressure Compressor*(Cooling ratio+(1-Cooling ratio)*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression))
T3 = P1*(q+(1-q)*(P2/P1)^((nc-1)/nc))
This formula uses 5 Variables
Variables Used
Discharge Temperature at high pressure compressor - (Measured in Kelvin) - Discharge Temperature at high pressure compressor is the temperature at which refrigerant leaves the compressor.
Suction Pressure of Low Pressure Compressor - (Measured in Pascal) - The Suction pressure of Low pressure compressor is the pressure of the refrigerant at the point where it enters the Low pressure compressor. It is also called Evaporator pressure.
Cooling ratio - The cooling ratio is defined as the ratio of heat abstracted by the cooling system to the heat abstracted to bring the refrigerant to the initial temperature.
Discharge Pressure of Low Pressure Compressor - (Measured in Pascal) - The Discharge pressure of Low pressure compressor is the pressure of the refrigerant at the point where it exits the Low-Pressure compressor. It is also called Pressure at the entry of intercooler.
Polytropic Index for Compression - Polytropic Index for Compression is that defined via a polytropic equation of state of the form P∝ρ1+1/n, where P is pressure, ρ is density, and n is the polytropic index.
STEP 1: Convert Input(s) to Base Unit
Suction Pressure of Low Pressure Compressor: 0.002 Bar --> 200 Pascal (Check conversion here)
Cooling ratio: 6 --> No Conversion Required
Discharge Pressure of Low Pressure Compressor: 7 Bar --> 700000 Pascal (Check conversion here)
Polytropic Index for Compression: 1.2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
T3 = P1*(q+(1-q)*(P2/P1)^((nc-1)/nc)) --> 200*(6+(1-6)*(700000/200)^((1.2-1)/1.2))
Evaluating ... ...
T3 = -2696.52984838796
STEP 3: Convert Result to Output's Unit
-2696.52984838796 Kelvin --> No Conversion Required
FINAL ANSWER
-2696.52984838796 -2696.529848 Kelvin <-- Discharge Temperature at high pressure compressor
(Calculation completed in 00.004 seconds)

Credits

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Abhishek Dharmendra Bansile has created this Calculator and 100+ more calculators!
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national institute of technology hamirpur (NITH ), hamirpur , himachal pradesh
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8 Minimum Work Required for a Two-Stage Reciprocating Compressor Calculators

Minimum Work required when Cooling Ratio is fixed
Go Work Required = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of refrigerant in kg per minute*[R]*((Suction temperature at Low pressure Compressor*(Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/(2*Polytropic Index for Compression))+Discharge Temperature of Refrigerant*(Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/(2*Polytropic Index for Compression))-Suction temperature at Low pressure Compressor-Discharge Temperature at high pressure compressor))
Minimum Work required when Temperature at end of Cooling in Intercooler is fixed
Go Work Required = 2*(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of refrigerant in kg per minute*[R]*Suction temperature at Low pressure Compressor*((Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/(2*Polytropic Index for Compression))-1)
Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect
Go Work Required = 2*(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of refrigerant in kg per minute*[R]*Suction Temperature of Refrigerant*((Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/(2*Polytropic Index for Compression))-1)
Suction Temperature at Low pressure compressor when Cooling ratio is constant
Go Suction temperature at Low pressure Compressor = Discharge Temperature at high pressure compressor/(Cooling ratio+(1-Cooling ratio)*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression))
Discharge Temperature at High pressure compressor when Cooling ratio is constant
Go Discharge Temperature at high pressure compressor = Suction Pressure of Low Pressure Compressor*(Cooling ratio+(1-Cooling ratio)*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression))
Suction Temperature at Low Pressure Compressor given Cooling Ratio
Go Suction temperature at Low pressure Compressor = ((Suction Temperature at High Pressure Compressor*Cooling ratio)-Suction Temperature at High Pressure Compressor+Discharge Temperature at high pressure compressor)/Cooling ratio
Cooling ratio
Go Cooling ratio = (Suction Temperature at High Pressure Compressor-Discharge Temperature at high pressure compressor)/(Suction Temperature at High Pressure Compressor-Suction temperature at Low pressure Compressor)
Discharge Temperature at High Pressure Compressor given Cooling Ratio
Go Discharge Temperature at high pressure compressor = Suction Temperature at High Pressure Compressor-Cooling ratio*(Suction Temperature at High Pressure Compressor-Suction temperature at Low pressure Compressor)

Discharge Temperature at High pressure compressor when Cooling ratio is constant Formula

Discharge Temperature at high pressure compressor = Suction Pressure of Low Pressure Compressor*(Cooling ratio+(1-Cooling ratio)*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression))
T3 = P1*(q+(1-q)*(P2/P1)^((nc-1)/nc))

What is Cooling ratio?

The cooling ratio is defined as the ratio of heat abstracted by the cooling system to the heat abstracted to bring the refrigerant to the initial temperature.

How to Calculate Discharge Temperature at High pressure compressor when Cooling ratio is constant?

Discharge Temperature at High pressure compressor when Cooling ratio is constant calculator uses Discharge Temperature at high pressure compressor = Suction Pressure of Low Pressure Compressor*(Cooling ratio+(1-Cooling ratio)*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)) to calculate the Discharge Temperature at high pressure compressor, The Discharge Temperature at High pressure compressor when Cooling ratio is constant formula is defined as the discharge temperature of refrigerant from the High pressure compressor when the cooling ratio is constant. Discharge Temperature at high pressure compressor is denoted by T3 symbol.

How to calculate Discharge Temperature at High pressure compressor when Cooling ratio is constant using this online calculator? To use this online calculator for Discharge Temperature at High pressure compressor when Cooling ratio is constant, enter Suction Pressure of Low Pressure Compressor (P1), Cooling ratio (q), Discharge Pressure of Low Pressure Compressor (P2) & Polytropic Index for Compression (nc) and hit the calculate button. Here is how the Discharge Temperature at High pressure compressor when Cooling ratio is constant calculation can be explained with given input values -> -2696.529848 = 200*(6+(1-6)*(700000/200)^((1.2-1)/1.2)).

FAQ

What is Discharge Temperature at High pressure compressor when Cooling ratio is constant?
The Discharge Temperature at High pressure compressor when Cooling ratio is constant formula is defined as the discharge temperature of refrigerant from the High pressure compressor when the cooling ratio is constant and is represented as T3 = P1*(q+(1-q)*(P2/P1)^((nc-1)/nc)) or Discharge Temperature at high pressure compressor = Suction Pressure of Low Pressure Compressor*(Cooling ratio+(1-Cooling ratio)*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)). The Suction pressure of Low pressure compressor is the pressure of the refrigerant at the point where it enters the Low pressure compressor. It is also called Evaporator pressure, The cooling ratio is defined as the ratio of heat abstracted by the cooling system to the heat abstracted to bring the refrigerant to the initial temperature, The Discharge pressure of Low pressure compressor is the pressure of the refrigerant at the point where it exits the Low-Pressure compressor. It is also called Pressure at the entry of intercooler & Polytropic Index for Compression is that defined via a polytropic equation of state of the form P∝ρ1+1/n, where P is pressure, ρ is density, and n is the polytropic index.
How to calculate Discharge Temperature at High pressure compressor when Cooling ratio is constant?
The Discharge Temperature at High pressure compressor when Cooling ratio is constant formula is defined as the discharge temperature of refrigerant from the High pressure compressor when the cooling ratio is constant is calculated using Discharge Temperature at high pressure compressor = Suction Pressure of Low Pressure Compressor*(Cooling ratio+(1-Cooling ratio)*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)). To calculate Discharge Temperature at High pressure compressor when Cooling ratio is constant, you need Suction Pressure of Low Pressure Compressor (P1), Cooling ratio (q), Discharge Pressure of Low Pressure Compressor (P2) & Polytropic Index for Compression (nc). With our tool, you need to enter the respective value for Suction Pressure of Low Pressure Compressor, Cooling ratio, Discharge Pressure of Low Pressure Compressor & Polytropic Index for Compression 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 Discharge Temperature at high pressure compressor?
In this formula, Discharge Temperature at high pressure compressor uses Suction Pressure of Low Pressure Compressor, Cooling ratio, Discharge Pressure of Low Pressure Compressor & Polytropic Index for Compression. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Discharge Temperature at high pressure compressor = Suction Temperature at High Pressure Compressor-Cooling ratio*(Suction Temperature at High Pressure Compressor-Suction temperature at Low pressure Compressor)
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