FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Minimum Work required when Cooling Ratio is fixed Formula

GoMinimum Work required when Temperature at end of Cooling in Intercooler is fixed Formula

GoMinimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Formula

Fx Copy

LaTeX Copy

Work required means work that is necessary in order to provide a covered service sought in connection application. Check FAQs

W = (\frac{n c}{n c - 1}) \cdot m \cdot [R] \cdot ((T 1 \cdot {(\frac{P 3}{P 1})}^{\frac{n c - 1}{2 \cdot n c}} + T d \cdot {(\frac{P 3}{P 1})}^{\frac{n c - 1}{2 \cdot n c}} - T 1 - T 3))

W - Work Required?n_c - Polytropic Index For Compression?m - Mass of Refrigerant in kg Per Minute?T₁ - Suction Temperature at Low Pressure Compressor?P₃ - Discharge Pressure of High Pressure Compressor?P₁ - Suction Pressure of Low Pressure Compressor?T_d - Discharge Temperature of Refrigerant?T₃ - Discharge Temperature at High Pressure Compressor?[R] - Universal gas constant?

Minimum Work required when Cooling Ratio is fixed Example

With values

With units

Only example

Here is how the Minimum Work required when Cooling Ratio is fixed equation looks like with Values.

Here is how the Minimum Work required when Cooling Ratio is fixed equation looks like with Units.

Here is how the Minimum Work required when Cooling Ratio is fixed equation looks like.

50.9477 = (\frac{1.2}{1.2 - 1}) \cdot 0.0304 \cdot 8.3145 \cdot ((300 \cdot {(\frac{15}{0.0024})}^{\frac{1.2 - 1}{2 \cdot 1.2}} + 970 \cdot {(\frac{15}{0.0024})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 300 - 310))

50.9477J = (\frac{1.2}{1.2 - 1}) \cdot 0.0304kg/min \cdot 8.3145 \cdot ((300K \cdot {(\frac{15Bar}{0.0024Bar})}^{\frac{1.2 - 1}{2 \cdot 1.2}} + 970K \cdot {(\frac{15Bar}{0.0024Bar})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 300K - 310K))

50.9477 = (\frac{1.2}{1.2 - 1}) \cdot 0.0304 \cdot 8.3145 \cdot ((300 \cdot {(\frac{15}{0.0024})}^{\frac{1.2 - 1}{2 \cdot 1.2}} + 970 \cdot {(\frac{15}{0.0024})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 300 - 310))

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Refrigeration and Air Conditioning » fx Minimum Work required when Cooling Ratio is fixed

Minimum Work required when Cooling Ratio is fixed Solution

Follow our step by step solution on how to calculate Minimum Work required when Cooling Ratio is fixed?

FIRST Step Consider the formula

W = (\frac{n c}{n c - 1}) \cdot m \cdot [R] \cdot ((T 1 \cdot {(\frac{P 3}{P 1})}^{\frac{n c - 1}{2 \cdot n c}} + T d \cdot {(\frac{P 3}{P 1})}^{\frac{n c - 1}{2 \cdot n c}} - T 1 - T 3))

Next Step Substitute values of Variables

∴

W = (\frac{1.2}{1.2 - 1}) \cdot 0.0304kg/min \cdot [R] \cdot ((300K \cdot {(\frac{15Bar}{0.0024Bar})}^{\frac{1.2 - 1}{2 \cdot 1.2}} + 970K \cdot {(\frac{15Bar}{0.0024Bar})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 300K - 310K))

Next Step Substitute values of Constants

∴

W = (\frac{1.2}{1.2 - 1}) \cdot 0.0304kg/min \cdot 8.3145 \cdot ((300K \cdot {(\frac{15Bar}{0.0024Bar})}^{\frac{1.2 - 1}{2 \cdot 1.2}} + 970K \cdot {(\frac{15Bar}{0.0024Bar})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 300K - 310K))

Next Step Convert Units

∴

W = (\frac{1.2}{1.2 - 1}) \cdot 0.0005kg/s \cdot 8.3145 \cdot ((300K \cdot {(\frac{1.5E+6Pa}{243Pa})}^{\frac{1.2 - 1}{2 \cdot 1.2}} + 970K \cdot {(\frac{1.5E+6Pa}{243Pa})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 300K - 310K))

Next Step Prepare to Evaluate

∴

W = (\frac{1.2}{1.2 - 1}) \cdot 0.0005 \cdot 8.3145 \cdot ((300 \cdot {(\frac{1.5E+6}{243})}^{\frac{1.2 - 1}{2 \cdot 1.2}} + 970 \cdot {(\frac{1.5E+6}{243})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 300 - 310))

Next Step Evaluate

∴

W = 50.9477457986318J

LAST Step Rounding Answer

∴

W = 50.9477J

Minimum Work required when Cooling Ratio is fixed Formula Elements

Variables

Constants

Work Required

Work required means work that is necessary in order to provide a covered service sought in connection application.

Symbol: W

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Work Required

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.

Symbol: n_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Polytropic Index For Compression

Mass of Refrigerant in kg Per Minute

Mass of Refrigerant in kg Per Minute is the mass on or by which the work is done.

Symbol: m

Measurement: Mass Flow RateUnit: kg/min

Note: Value should be greater than 0.

Formulas to find Mass of Refrigerant in kg Per Minute

Suction Temperature at Low Pressure Compressor

Suction Temperature at Low Pressure Compressor is the temperature of the refrigerant at the inlet or during the suction stroke.

Symbol: T₁

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Suction Temperature at Low Pressure Compressor

Discharge Pressure of High Pressure Compressor

Discharge Pressure of High Pressure Compressor is the pressure of the refrigerant at the point where it exits the High Pressure compressor. It is also called Condenser Pressure.

Symbol: P₃

Measurement: PressureUnit: Bar

Note: Value can be positive or negative.

Formulas to find Discharge Pressure of High Pressure Compressor

Suction Pressure of Low Pressure Compressor

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.

Symbol: P₁

Measurement: PressureUnit: Bar

Note: Value can be positive or negative.

Formulas to find Suction Pressure of Low Pressure Compressor

Discharge Temperature of Refrigerant

Discharge Temperature of Refrigerant is the temperature of refrigerant at the outlet or during the discharge stroke.

Symbol: T_d

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Discharge Temperature of Refrigerant

Discharge Temperature at High Pressure Compressor

Discharge Temperature at High Pressure Compressor is the temperature at which refrigerant leaves the compressor.

Symbol: T₃

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Discharge Temperature at High Pressure Compressor

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

Other Formulas to find Work Required

Go Minimum Work required when Temperature at end of Cooling in Intercooler is fixed

W = 2 \cdot (\frac{n c}{n c - 1}) \cdot m \cdot [R] \cdot T 1 \cdot ({(\frac{P 3}{P 1})}^{\frac{n c - 1}{2 \cdot n c}} - 1)

Go Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect

W = 2 \cdot (\frac{n c}{n c - 1}) \cdot m \cdot [R] \cdot T r \cdot ({(\frac{P 3}{P 1})}^{\frac{n c - 1}{2 \cdot n c}} - 1)

Other formulas in Minimum Work category

Go Cooling ratio

q = \frac{T 2 - T 3}{T 2 - T 1}

Go Discharge Temperature at High Pressure Compressor given Cooling Ratio

T 3 = T 2 - q \cdot (T 2 - T 1)

How to Evaluate Minimum Work required when Cooling Ratio is fixed?

Minimum Work required when Cooling Ratio is fixed evaluator uses 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)) to evaluate the Work Required, Minimum Work required when Cooling Ratio is fixed formula is defined as the minimum energy required to cool a system when the cooling ratio is fixed, which is essential in various industrial and engineering applications where efficient cooling systems are crucial. Work Required is denoted by W symbol.

How to evaluate Minimum Work required when Cooling Ratio is fixed using this online evaluator? To use this online evaluator for Minimum Work required when Cooling Ratio is fixed, enter Polytropic Index For Compression (n_c), Mass of Refrigerant in kg Per Minute (m), Suction Temperature at Low Pressure Compressor (T₁), Discharge Pressure of High Pressure Compressor (P₃), Suction Pressure of Low Pressure Compressor (P₁), Discharge Temperature of Refrigerant (T_d) & Discharge Temperature at High Pressure Compressor (T₃) and hit the calculate button.

FAQs on Minimum Work required when Cooling Ratio is fixed

What is the formula to find Minimum Work required when Cooling Ratio is fixed?

The formula of Minimum Work required when Cooling Ratio is fixed is expressed as 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)). Here is an example- 23.78254 = (1.2/(1.2-1))*0.000506*[R]*((300*(1500000/243)^((1.2-1)/(2*1.2))+970*(1500000/243)^((1.2-1)/(2*1.2))-300-310)).

How to calculate Minimum Work required when Cooling Ratio is fixed?

With Polytropic Index For Compression (n_c), Mass of Refrigerant in kg Per Minute (m), Suction Temperature at Low Pressure Compressor (T₁), Discharge Pressure of High Pressure Compressor (P₃), Suction Pressure of Low Pressure Compressor (P₁), Discharge Temperature of Refrigerant (T_d) & Discharge Temperature at High Pressure Compressor (T₃) we can find Minimum Work required when Cooling Ratio is fixed using the formula - 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)). This formula also uses Universal gas constant .

What are the other ways to Calculate Work Required?

Here are the different ways to Calculate Work Required-

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)
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)

Can the Minimum Work required when Cooling Ratio is fixed be negative?

Yes, the Minimum Work required when Cooling Ratio is fixed, measured in Energy can be negative.

Which unit is used to measure Minimum Work required when Cooling Ratio is fixed?

Minimum Work required when Cooling Ratio is fixed is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Minimum Work required when Cooling Ratio is fixed can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Minimum Work required when Cooling Ratio is fixed Formula

​GoMinimum Work required when Temperature at end of Cooling in Intercooler is fixed Formula

​GoMinimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Formula

Minimum Work required when Cooling Ratio is fixed Example

Minimum Work required when Cooling Ratio is fixed Solution

Minimum Work required when Cooling Ratio is fixed Formula Elements

Other Formulas to find Work Required

Other formulas in Minimum Work category

How to Evaluate Minimum Work required when Cooling Ratio is fixed?

FAQs on Minimum Work required when Cooling Ratio is fixed

Variable Name

GoMinimum Work required when Temperature at end of Cooling in Intercooler is fixed Formula

GoMinimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Formula