Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness Calculator

⤿

Air-Standard Cycles

Design of IC Engine Components

Engine Performance Parameters

Fuel Injection in IC Engine

Fundamentals of IC Engine

✖Compression ratio refers to how much the air-fuel mixture is squeezed in the cylinder before ignition. It's essentially the ratio between the volume of the cylinder at BDC to TDC.ⓘ Compression Ratio [r]			+10% -10%
✖Final Temperature can be referred as the temperature of cylinder after ignition or final temperature of the charge before work is extracted. It is measured in absolute temperature (kelvin-scale).ⓘ Final Temperature [T_f]			+10% -10%
✖Initial Temperature can be referred as the temperature of cylinder after intake stroke or initial temperature of the charge. It is measured in absolute temperature (Kelvin-scale).ⓘ Initial Temperature [T_i]			+10% -10%
✖Molar Specific Heat Capacity at Constant Volume is the amount of heat required to raise the temperature of one mol of the gas by one degree at constant volume.ⓘ Molar Specific Heat Capacity at Constant Volume [C_v]			+10% -10%
✖The effectiveness of heat exchanger is a ratio of actual heat transfer to the maximum possible transfer in ideal scenario. It reflects how well a device extracts heat from higher to lower sink.ⓘ Effectiveness of Heat Exchanger [ε]			+10% -10%

✖The Thermal Efficiency of Stirling Cycle represents the effectiveness of Stirling engine. It is measured by comparing how much work is done through out the system to the heat supplied to the system.ⓘ Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness [η_s]

⎘ Copy

👎

Formula

✖

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness

Formula

`"η"_{"s"} = 100*(("[R]"*ln("r")*("T"_{"f"}-"T"_{"i"}))/("[R]"*"T"_{"f"}*ln("r")+"C"_{"v"}*(1-"ε")*("T"_{"f"}-"T"_{"i"})))`

Example

`"19.88537"=100*(("[R]"*ln("20")*("423K"-"283K"))/("[R]"*"423K"*ln("20")+"100J/K*mol"*(1-"0.5")*("423K"-"283K")))`

Calculator

LaTeX

Reset

👍

Download Air-Standard Cycles Formulas PDF PDF Image

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness Solution

STEP 0: Pre-Calculation Summary

Formula Used

Thermal Efficiency of Stirling Cycle = 100*(([R]*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/([R]*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature)))
η_s = 100*(([R]*ln(r)*(T_f-T_i))/([R]*T_f*ln(r)+C_v*(1-ε)*(T_f-T_i)))
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Thermal Efficiency of Stirling Cycle - The Thermal Efficiency of Stirling Cycle represents the effectiveness of Stirling engine. It is measured by comparing how much work is done through out the system to the heat supplied to the system.
Compression Ratio - Compression ratio refers to how much the air-fuel mixture is squeezed in the cylinder before ignition. It's essentially the ratio between the volume of the cylinder at BDC to TDC.
Final Temperature - (Measured in Kelvin) - Final Temperature can be referred as the temperature of cylinder after ignition or final temperature of the charge before work is extracted. It is measured in absolute temperature (kelvin-scale).
Initial Temperature - (Measured in Kelvin) - Initial Temperature can be referred as the temperature of cylinder after intake stroke or initial temperature of the charge. It is measured in absolute temperature (Kelvin-scale).
Molar Specific Heat Capacity at Constant Volume - (Measured in Joule Per Kelvin Per Mole) - Molar Specific Heat Capacity at Constant Volume is the amount of heat required to raise the temperature of one mol of the gas by one degree at constant volume.
Effectiveness of Heat Exchanger - The effectiveness of heat exchanger is a ratio of actual heat transfer to the maximum possible transfer in ideal scenario. It reflects how well a device extracts heat from higher to lower sink.

STEP 1: Convert Input(s) to Base Unit

Compression Ratio: 20 --> No Conversion Required
Final Temperature: 423 Kelvin --> 423 Kelvin No Conversion Required
Initial Temperature: 283 Kelvin --> 283 Kelvin No Conversion Required
Molar Specific Heat Capacity at Constant Volume: 100 Joule Per Kelvin Per Mole --> 100 Joule Per Kelvin Per Mole No Conversion Required
Effectiveness of Heat Exchanger: 0.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η_s = 100*(([R]*ln(r)*(T_f-T_i))/([R]*T_f*ln(r)+C_v*(1-ε)*(T_f-T_i))) --> 100*(([R]*ln(20)*(423-283))/([R]*423*ln(20)+100*(1-0.5)*(423-283)))

Evaluating ... ...

η_s = 19.8853668537813

STEP 3: Convert Result to Output's Unit

19.8853668537813 --> No Conversion Required

FINAL ANSWER

19.8853668537813 ≈ 19.88537 <-- Thermal Efficiency of Stirling Cycle

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » IC Engine » Air-Standard Cycles » Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness

Credits

Created by Aditya Prakash Gautam

Indian Institute of Technology (IIT (ISM) ), Dhanbad, Jharkhand

Aditya Prakash Gautam has created this Calculator and 25+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Calculator and 2500+ more calculators!

< 18 Air-Standard Cycles Calculators

Mean Effective Pressure in Dual Cycle

Go Mean Effective Pressure of Dual Cycle = Pressure at Start of Isentropic Compression*(Compression Ratio^Heat Capacity Ratio*((Pressure Ratio in Dual Cycle-1)+Heat Capacity Ratio*Pressure Ratio in Dual Cycle*(Cut-off Ratio-1))-Compression Ratio*(Pressure Ratio in Dual Cycle*Cut-off Ratio^Heat Capacity Ratio-1))/((Heat Capacity Ratio-1)*(Compression Ratio-1))

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness

Go Thermal Efficiency of Stirling Cycle = 100*(([R]*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/([R]*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature)))

Work Output for Dual Cycle

Go Work Output of Dual Cycle = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*Pressure Ratio*(Cut-off Ratio-1)+(Pressure Ratio-1))-(Pressure Ratio*Cut-off Ratio^(Heat Capacity Ratio)-1))/(Heat Capacity Ratio-1)

Work Output for Diesel Cycle

Go Work Output of Diesel Cycle = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*(Cut-off Ratio-1)-Compression Ratio^(1-Heat Capacity Ratio)*(Cut-off Ratio^(Heat Capacity Ratio)-1)))/(Heat Capacity Ratio-1)

Mean Effective Pressure in Diesel Cycle

Go Mean Effective Pressure of Diesel Cycle = Pressure at Start of Isentropic Compression*(Heat Capacity Ratio*Compression Ratio^Heat Capacity Ratio*(Cut-off Ratio-1)-Compression Ratio*(Cut-off Ratio^Heat Capacity Ratio-1))/((Heat Capacity Ratio-1)*(Compression Ratio-1))

Thermal Efficiency of Dual Cycle

Go Thermal Efficiency of Dual Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*((Pressure Ratio in Dual Cycle*Cut-off Ratio^Heat Capacity Ratio-1)/(Pressure Ratio in Dual Cycle-1+Pressure Ratio in Dual Cycle*Heat Capacity Ratio*(Cut-off Ratio-1))))

Mean Effective Pressure in Otto Cycle

Go Mean Effective Pressure of Otto Cycle = Pressure at Start of Isentropic Compression*Compression Ratio*(((Compression Ratio^(Heat Capacity Ratio-1)-1)*(Pressure Ratio-1))/((Compression Ratio-1)*(Heat Capacity Ratio-1)))

Thermal Efficiency of Atkinson Cycle

Go Thermal Efficiency of Atkinson Cycle = 100*(1-Heat Capacity Ratio*((Expansion Ratio-Compression Ratio)/(Expansion Ratio^(Heat Capacity Ratio)-Compression Ratio^(Heat Capacity Ratio))))

Work Output for Otto Cycle

Go Work Output of Otto Cycle = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*((Pressure Ratio-1)*(Compression Ratio^(Heat Capacity Ratio-1)-1))/(Heat Capacity Ratio-1)

Air Standard Efficiency for Diesel Engines

Go Efficiency of Diesel Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cut-off Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cut-off Ratio-1)))

Thermal Efficiency of Diesel Cycle

Go Thermal Efficiency of Diesel Cycle = 1-1/Compression Ratio^(Heat Capacity Ratio-1)*(Cut-off Ratio^Heat Capacity Ratio-1)/(Heat Capacity Ratio*(Cut-off Ratio-1))

Thermal Efficiency of Lenoir Cycle

Go Thermal Efficiency of Lenoir Cycle = 100*(1-Heat Capacity Ratio*((Pressure Ratio^(1/Heat Capacity Ratio)-1)/(Pressure Ratio-1)))

Thermal Efficiency of Ericsson Cycle

Go Thermal Efficiency of Ericsson Cycle = (Higher Temperature-Lower Temperature)/(Higher Temperature)

Air Standard Efficiency for Petrol engines

Go Efficiency of Otto Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1)))

Thermal Efficiency of Otto Cycle

Go Thermal Efficiency of Otto Cycle = 1-1/Compression Ratio^(Heat Capacity Ratio-1)

Relative Air-Fuel Ratio

Go Relative Air Fuel Ratio = Actual Air Fuel Ratio/Stoichiometric Air Fuel Ratio

Air Standard Efficiency given Relative Efficiency

Go Efficiency = Indicated Thermal Efficiency/Relative Efficiency

Actual Air Fuel Ratio

Go Actual Air Fuel Ratio = Mass of Air/Mass of Fuel

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness Formula

What is Stirling cycle ?

The Carnot cycle has a low mean effective pressure because of its very low work output. Hence, one of the modified forms of the cycle to produce higher mean effective pressure whilst theoretically achieving full Carnot cycle efficiency is the 'Stirling cycle'. The thermal efficiency of Stirling engines is 40% while the efficiency of similar Otto and Diesel engines are 25 and 35%, respectively.

How to Calculate Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness?

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness calculator uses Thermal Efficiency of Stirling Cycle = 100*(([R]*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/([R]*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature))) to calculate the Thermal Efficiency of Stirling Cycle, Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness refers to how effectively a Stirling engine converts heat energy from fuel into mechanical work. It reflects the effectiveness of converting heat from burning fuel into usable work output at crankshaft. It takes into account the compression ratio as well as heat exchanger effectiveness. Thermal Efficiency of Stirling Cycle is denoted by η_s symbol.

How to calculate Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness using this online calculator? To use this online calculator for Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness, enter Compression Ratio (r), Final Temperature (T_f), Initial Temperature (T_i), Molar Specific Heat Capacity at Constant Volume (C_v) & Effectiveness of Heat Exchanger (ε) and hit the calculate button. Here is how the Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness calculation can be explained with given input values -> 19.88537 = 100*(([R]*ln(20)*(423-283))/([R]*423*ln(20)+100*(1-0.5)*(423-283))).

FAQ

What is Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness?

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness refers to how effectively a Stirling engine converts heat energy from fuel into mechanical work. It reflects the effectiveness of converting heat from burning fuel into usable work output at crankshaft. It takes into account the compression ratio as well as heat exchanger effectiveness and is represented as η_s = 100*(([R]*ln(r)*(T_f-T_i))/([R]*T_f*ln(r)+C_v*(1-ε)*(T_f-T_i))) or Thermal Efficiency of Stirling Cycle = 100*(([R]*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/([R]*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature))). Compression ratio refers to how much the air-fuel mixture is squeezed in the cylinder before ignition. It's essentially the ratio between the volume of the cylinder at BDC to TDC, Final Temperature can be referred as the temperature of cylinder after ignition or final temperature of the charge before work is extracted. It is measured in absolute temperature (kelvin-scale), Initial Temperature can be referred as the temperature of cylinder after intake stroke or initial temperature of the charge. It is measured in absolute temperature (Kelvin-scale), Molar Specific Heat Capacity at Constant Volume is the amount of heat required to raise the temperature of one mol of the gas by one degree at constant volume & The effectiveness of heat exchanger is a ratio of actual heat transfer to the maximum possible transfer in ideal scenario. It reflects how well a device extracts heat from higher to lower sink.

How to calculate Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness?

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness refers to how effectively a Stirling engine converts heat energy from fuel into mechanical work. It reflects the effectiveness of converting heat from burning fuel into usable work output at crankshaft. It takes into account the compression ratio as well as heat exchanger effectiveness is calculated using Thermal Efficiency of Stirling Cycle = 100*(([R]*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/([R]*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature))). To calculate Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness, you need Compression Ratio (r), Final Temperature (T_f), Initial Temperature (T_i), Molar Specific Heat Capacity at Constant Volume (C_v) & Effectiveness of Heat Exchanger (ε). With our tool, you need to enter the respective value for Compression Ratio, Final Temperature, Initial Temperature, Molar Specific Heat Capacity at Constant Volume & Effectiveness of Heat Exchanger and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search