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Work done during Isothermal Compression given Volume and Pressure Ratio Formula

GoWork done during Isothermal Compression given Temperature and Compression Ratio Formula

GoWork done during Isothermal Compression given Temperature and Volume Ratio Formula

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Work done per minute during Isothermal Compression is the energy transferred per minute during the isothermal compression of a gas in a single stage compressor. Check FAQs

W Isothermal = 2.3 \cdot P 1 \cdot V 1 \cdot \ln (\frac{P 2}{P 1})

W_Isothermal - Work done per minute during Isothermal Compression?P₁ - Suction Pressure?V₁ - Suction Volume?P₂ - Discharge Pressure of Refrigerant?

Work done during Isothermal Compression given Volume and Pressure Ratio Example

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Here is how the Work done during Isothermal Compression given Volume and Pressure Ratio equation looks like with Values.

Here is how the Work done during Isothermal Compression given Volume and Pressure Ratio equation looks like with Units.

Here is how the Work done during Isothermal Compression given Volume and Pressure Ratio equation looks like.

4814.7973 = 2.3 \cdot 1.013 \cdot 10 \cdot \ln (\frac{8}{1.013})

4814.7973KJ = 2.3 \cdot 1.013Bar \cdot 10m³ \cdot \ln (\frac{8Bar}{1.013Bar})

4814.7973 = 2.3 \cdot 1.013 \cdot 10 \cdot \ln (\frac{8}{1.013})

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Work done during Isothermal Compression given Volume and Pressure Ratio Solution

Follow our step by step solution on how to calculate Work done during Isothermal Compression given Volume and Pressure Ratio?

FIRST Step Consider the formula

W Isothermal = 2.3 \cdot P 1 \cdot V 1 \cdot \ln (\frac{P 2}{P 1})

Next Step Substitute values of Variables

∴

W Isothermal = 2.3 \cdot 1.013Bar \cdot 10m³ \cdot \ln (\frac{8Bar}{1.013Bar})

Next Step Convert Units

∴

W Isothermal = 2.3 \cdot 101300Pa \cdot 10m³ \cdot \ln (\frac{800000Pa}{101300Pa})

Next Step Prepare to Evaluate

∴

W Isothermal = 2.3 \cdot 101300 \cdot 10 \cdot \ln (\frac{800000}{101300})

Next Step Evaluate

∴

W Isothermal = 4814797.33471132J

Next Step Convert to Output's Unit

∴

W Isothermal = 4814.79733471132KJ

LAST Step Rounding Answer

∴

W Isothermal = 4814.7973KJ

Work done during Isothermal Compression given Volume and Pressure Ratio Formula Elements

Variables

Functions

Work done per minute during Isothermal Compression

Work done per minute during Isothermal Compression is the energy transferred per minute during the isothermal compression of a gas in a single stage compressor.

Symbol: W_Isothermal

Measurement: EnergyUnit: KJ

Note: Value can be positive or negative.

Formulas to find Work done per minute during Isothermal Compression

Suction Pressure

Suction pressure is the pressure of the fluid at the inlet of a compressor, which affects the compressor's performance and work done.

Symbol: P₁

Measurement: PressureUnit: Bar

Note: Value can be positive or negative.

Formulas to find Suction Pressure

Suction Volume

Suction volume is the volume of air drawn into the compressor's cylinder during the suction stroke of a single stage compression process.

Symbol: V₁

Measurement: VolumeUnit: m³

Note: Value can be positive or negative.

Formulas to find Suction Volume

Discharge Pressure of Refrigerant

Discharge Pressure of Refrigerant is the pressure of refrigerant at the outlet of a single stage compressor after work is done on it.

Symbol: P₂

Measurement: PressureUnit: Bar

Note: Value can be positive or negative.

Formulas to find Discharge Pressure of Refrigerant

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other Formulas to find Work done per minute during Isothermal Compression

Go Work done during Isothermal Compression given Temperature and Compression Ratio

W Isothermal = 2.3 \cdot m gas \cdot [R] \cdot T 1 \cdot \ln (r)

Go Work done during Isothermal Compression given Temperature and Volume Ratio

W Isothermal = 2.3 \cdot m \cdot [R] \cdot T \cdot \ln (\frac{V 1}{V 2})

Go Work done during Isothermal Compression given Temperature and Pressure Ratio

W Isothermal = 2.3 \cdot m \cdot [R] \cdot T \cdot \ln (\frac{P 2}{P 1})

Go Work done during Isothermal Compression given Pressure and Volume Ratio

W Isothermal = 2.3 \cdot P 1 \cdot V 1 \cdot \ln (\frac{V 1}{V 2})

Other formulas in Work Done by Single Stage Compressor category

Go Work done during polytropic compression

W Polytropic = (\frac{n}{n - 1}) \cdot m \cdot [R] \cdot (T discharge - T refrigerant)

Go Work done during isentropic Compression given Specific Heat Capacity Constant Pressure

W Isentropic = m \cdot C p \cdot (T discharge - T refrigerant)

Go Work done during isentropic compression

W Isentropic = (\frac{γ}{γ - 1}) \cdot m \cdot [R] \cdot (T discharge - T refrigerant)

How to Evaluate Work done during Isothermal Compression given Volume and Pressure Ratio?

Work done during Isothermal Compression given Volume and Pressure Ratio evaluator uses Work done per minute during Isothermal Compression = 2.3*Suction Pressure*Suction Volume*ln(Discharge Pressure of Refrigerant/Suction Pressure) to evaluate the Work done per minute during Isothermal Compression, Work done during Isothermal Compression given Volume and Pressure Ratio formula is defined as the energy transferred during the compression process in an isothermal system, where the temperature remains constant, and is a crucial parameter in understanding the performance of a single-stage compressor. Work done per minute during Isothermal Compression is denoted by W_Isothermal symbol.

How to evaluate Work done during Isothermal Compression given Volume and Pressure Ratio using this online evaluator? To use this online evaluator for Work done during Isothermal Compression given Volume and Pressure Ratio, enter Suction Pressure (P₁), Suction Volume (V₁) & Discharge Pressure of Refrigerant (P₂) and hit the calculate button.

FAQs on Work done during Isothermal Compression given Volume and Pressure Ratio

What is the formula to find Work done during Isothermal Compression given Volume and Pressure Ratio?

The formula of Work done during Isothermal Compression given Volume and Pressure Ratio is expressed as Work done per minute during Isothermal Compression = 2.3*Suction Pressure*Suction Volume*ln(Discharge Pressure of Refrigerant/Suction Pressure). Here is an example- 4.814797 = 2.3*101300*10*ln(800000/101300).

How to calculate Work done during Isothermal Compression given Volume and Pressure Ratio?

With Suction Pressure (P₁), Suction Volume (V₁) & Discharge Pressure of Refrigerant (P₂) we can find Work done during Isothermal Compression given Volume and Pressure Ratio using the formula - Work done per minute during Isothermal Compression = 2.3*Suction Pressure*Suction Volume*ln(Discharge Pressure of Refrigerant/Suction Pressure). This formula also uses Natural Logarithm (ln) function(s).

What are the other ways to Calculate Work done per minute during Isothermal Compression?

Here are the different ways to Calculate Work done per minute during Isothermal Compression-

Work done per minute during Isothermal Compression=2.3*Mass of Gas*[R]*Temperature of Gas 1*ln(Compression Ratio)
Work done per minute during Isothermal Compression=2.3*Mass of Refrigerant in kg per minute*[R]*Temperature of Refrigerant*ln(Suction Volume/Discharge Volume)
Work done per minute during Isothermal Compression=2.3*Mass of Refrigerant in kg per minute*[R]*Temperature of Refrigerant*ln(Discharge Pressure of Refrigerant/Suction Pressure)

Can the Work done during Isothermal Compression given Volume and Pressure Ratio be negative?

Yes, the Work done during Isothermal Compression given Volume and Pressure Ratio, measured in Energy can be negative.

Which unit is used to measure Work done during Isothermal Compression given Volume and Pressure Ratio?

Work done during Isothermal Compression given Volume and Pressure Ratio is usually measured using the Kilojoule[KJ] for Energy. Joule[KJ], Gigajoule[KJ], Megajoule[KJ] are the few other units in which Work done during Isothermal Compression given Volume and Pressure Ratio can be measured.

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Work done during Isothermal Compression given Volume and Pressure Ratio Formula

​GoWork done during Isothermal Compression given Temperature and Compression Ratio Formula

​GoWork done during Isothermal Compression given Temperature and Volume Ratio Formula

Work done during Isothermal Compression given Volume and Pressure Ratio Example

Work done during Isothermal Compression given Volume and Pressure Ratio Solution

Work done during Isothermal Compression given Volume and Pressure Ratio Formula Elements

Other Formulas to find Work done per minute during Isothermal Compression

Other formulas in Work Done by Single Stage Compressor category

How to Evaluate Work done during Isothermal Compression given Volume and Pressure Ratio?

FAQs on Work done during Isothermal Compression given Volume and Pressure Ratio

Variable Name

GoWork done during Isothermal Compression given Temperature and Compression Ratio Formula

GoWork done during Isothermal Compression given Temperature and Volume Ratio Formula