Energy Performance Ratio of Heat Pump Calculator

✖Heat Delivered to Hot Body is the amount of heat transferred to a body by doing some work.ⓘ Heat Delivered to Hot Body [Q_delivered]			+10% -10%
✖Work Done per min is when a force that is applied to an object moves that object.ⓘ Work Done per min [W_{per min}]			+10% -10%

✖Theoretical Coefficient of Performance of a refrigerator is the ratio of heat Extracted from the Refrigerator to the amount of work done.ⓘ Energy Performance Ratio of Heat Pump [COP_theoretical]

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Formula

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Energy Performance Ratio of Heat Pump

Formula

`"COP"_{"theoretical"} = "Q"_{"delivered"}/"W"_{"per min"}`

Example

`"4.807692"="1250kJ/min"/"260kJ/min"`

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Energy Performance Ratio of Heat Pump Solution

STEP 0: Pre-Calculation Summary

Formula Used

Theoretical Coefficient of Performance = Heat Delivered to Hot Body/Work Done per min
COP_theoretical = Q_delivered/W_{per min}
This formula uses 3 Variables

Variables Used

Theoretical Coefficient of Performance - Theoretical Coefficient of Performance of a refrigerator is the ratio of heat Extracted from the Refrigerator to the amount of work done.
Heat Delivered to Hot Body - (Measured in Watt) - Heat Delivered to Hot Body is the amount of heat transferred to a body by doing some work.
Work Done per min - (Measured in Watt) - Work Done per min is when a force that is applied to an object moves that object.

STEP 1: Convert Input(s) to Base Unit

Heat Delivered to Hot Body: 1250 Kilojoule per Minute --> 20833.3333333334 Watt (Check conversion here)
Work Done per min: 260 Kilojoule per Minute --> 4333.33333333334 Watt (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

COP_theoretical = Q_delivered/W_{per min} --> 20833.3333333334/4333.33333333334

Evaluating ... ...

COP_theoretical = 4.80769230769232

STEP 3: Convert Result to Output's Unit

4.80769230769232 --> No Conversion Required

FINAL ANSWER

4.80769230769232 ≈ 4.807692 <-- Theoretical Coefficient of Performance

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Refrigeration and Air Conditioning » Air Refrigeration Cycles » Energy Performance Ratio of Heat Pump

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 Mayank Tayal

National Institute of Technology (NIT), Durgapur

Mayank Tayal has verified this Calculator and 10+ more calculators!

< 8 Air Refrigeration Cycles Calculators

COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index

Go Theoretical Coefficient of Performance = (Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)/((Polytropic Index/(Polytropic Index-1))*((Heat Capacity Ratio-1)/Heat Capacity Ratio)*((Ideal Temp at end of Isentropic Compression-Ideal Temp at end of Isobaric Cooling)-(Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)))

Heat Absorbed during Constant Pressure Expansion Process

Go Heat Absorbed = Specific Heat Capacity at Constant Pressure*(Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)

Heat Rejected during Constant pressure Cooling Process

Go Heat Rejected = Specific Heat Capacity at Constant Pressure*(Ideal Temp at end of Isentropic Compression-Ideal Temp at end of Isobaric Cooling)

COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index

Go Theoretical Coefficient of Performance = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)

Compression or Expansion Ratio

Go Compression or Expansion Ratio = Pressure at End of Isentropic Compression/Pressure at Start of Isentropic Compression

Relative Coefficient of Performance

Go Relative Coefficient of Performance = Actual Coefficient of Performance/Theoretical Coefficient of Performance

Energy Performance Ratio of Heat Pump

Go Theoretical Coefficient of Performance = Heat Delivered to Hot Body/Work Done per min

Theoretical Coefficient of Performance of Refrigerator

Go Theoretical Coefficient of Performance = Heat Extracted from Refrigerator/Work Done

< 8 Air Refrigeration Cycles Calculators

COP of Bell-Coleman Cycle for given Temperatures, Polytropic Index and Adiabatic Index

Heat Absorbed during Constant Pressure Expansion Process

Go Heat Absorbed = Specific Heat Capacity at Constant Pressure*(Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)

Heat Rejected during Constant pressure Cooling Process

Go Heat Rejected = Specific Heat Capacity at Constant Pressure*(Ideal Temp at end of Isentropic Compression-Ideal Temp at end of Isobaric Cooling)

COP of Bell-Coleman Cycle for given Compression Ratio and Adiabatic Index

Go Theoretical Coefficient of Performance = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)

Compression or Expansion Ratio

Go Compression or Expansion Ratio = Pressure at End of Isentropic Compression/Pressure at Start of Isentropic Compression

Relative Coefficient of Performance

Go Relative Coefficient of Performance = Actual Coefficient of Performance/Theoretical Coefficient of Performance

Energy Performance Ratio of Heat Pump

Go Theoretical Coefficient of Performance = Heat Delivered to Hot Body/Work Done per min

Theoretical Coefficient of Performance of Refrigerator

Go Theoretical Coefficient of Performance = Heat Extracted from Refrigerator/Work Done

Energy Performance Ratio of Heat Pump Formula

Theoretical Coefficient of Performance = Heat Delivered to Hot Body/Work Done per min
COP_theoretical = Q_delivered/W_{per min}

What is Energy Performance Ratio (EPR) ?

It is the ratio of heat delivered to the body and work required to be done on the system. It is also called COP of the heat engine.

How to Calculate Energy Performance Ratio of Heat Pump?

Energy Performance Ratio of Heat Pump calculator uses Theoretical Coefficient of Performance = Heat Delivered to Hot Body/Work Done per min to calculate the Theoretical Coefficient of Performance, The Energy Performance Ratio of Heat Pump formula is defined as the ratio of the amount of heat delivered to the hot body to the amount of work required to be done on the system. Theoretical Coefficient of Performance is denoted by COP_theoretical symbol.

How to calculate Energy Performance Ratio of Heat Pump using this online calculator? To use this online calculator for Energy Performance Ratio of Heat Pump, enter Heat Delivered to Hot Body (Q_delivered) & Work Done per min (W_{per min}) and hit the calculate button. Here is how the Energy Performance Ratio of Heat Pump calculation can be explained with given input values -> 4.807692 = 20833.3333333334/4333.33333333334.

FAQ

What is Energy Performance Ratio of Heat Pump?

The Energy Performance Ratio of Heat Pump formula is defined as the ratio of the amount of heat delivered to the hot body to the amount of work required to be done on the system and is represented as COP_theoretical = Q_delivered/W_{per min} or Theoretical Coefficient of Performance = Heat Delivered to Hot Body/Work Done per min. Heat Delivered to Hot Body is the amount of heat transferred to a body by doing some work & Work Done per min is when a force that is applied to an object moves that object.

How to calculate Energy Performance Ratio of Heat Pump?

The Energy Performance Ratio of Heat Pump formula is defined as the ratio of the amount of heat delivered to the hot body to the amount of work required to be done on the system is calculated using Theoretical Coefficient of Performance = Heat Delivered to Hot Body/Work Done per min. To calculate Energy Performance Ratio of Heat Pump, you need Heat Delivered to Hot Body (Q_delivered) & Work Done per min (W_{per min}). With our tool, you need to enter the respective value for Heat Delivered to Hot Body & Work Done per min 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 Theoretical Coefficient of Performance?

In this formula, Theoretical Coefficient of Performance uses Heat Delivered to Hot Body & Work Done per min. We can use 6 other way(s) to calculate the same, which is/are as follows -

Theoretical Coefficient of Performance = Heat Extracted from Refrigerator/Work Done
Theoretical Coefficient of Performance = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)
Theoretical Coefficient of Performance = (Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)/((Polytropic Index/(Polytropic Index-1))*((Heat Capacity Ratio-1)/Heat Capacity Ratio)*((Ideal Temp at end of Isentropic Compression-Ideal Temp at end of Isobaric Cooling)-(Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)))
Theoretical Coefficient of Performance = Heat Extracted from Refrigerator/Work Done
Theoretical Coefficient of Performance = 1/(Compression or Expansion Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)
Theoretical Coefficient of Performance = (Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)/((Polytropic Index/(Polytropic Index-1))*((Heat Capacity Ratio-1)/Heat Capacity Ratio)*((Ideal Temp at end of Isentropic Compression-Ideal Temp at end of Isobaric Cooling)-(Temperature at Start of Isentropic Compression-Temperature at End of Isentropic Expansion)))

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