Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness Solution

STEP 0: Pre-Calculation Summary
Formula Used
Thermal Efficiency of Stirling Cycle = 100*((Universal Gas Constant*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/(Universal Gas Constant*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature)))
ηstirling = 100*((R*ln(r)*(Tf-Ti))/(R*Tf*ln(r)+Cv*(1-ϵ)*(Tf-Ti)))
This formula uses 1 Functions, 7 Variables
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 (in %) represents the fraction of heat converted into useful work in an engine working on the Stirling cycle.
Universal Gas Constant - Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joule*kelvin−1*mole−1.
Compression Ratio - Compression ratio is ratio between volume of cylinder and combustion chamber.
Final Temperature - (Measured in Kelvin) - Final Temperature is the measure of hotness or coldness of a system at its final state.
Initial Temperature - (Measured in Kelvin) - Initial Temperature is the measure of hotness or coldness of a system at its initial state.
Molar Specific Heat Capacity at Constant Volume - (Measured in Joule Per Kelvin Per Mole) - Molar Specific Heat Capacity at Constant Volume , Cv ( of a gas ) is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant volume.
Effectiveness of Heat Exchanger - The effectiveness of heat exchanger is defined as the ratio of the actual heat transfer to the maximum possible heat transfer.
STEP 1: Convert Input(s) to Base Unit
Universal Gas Constant: 8.314 --> No Conversion Required
Compression Ratio: 1.75 --> No Conversion Required
Final Temperature: 345 Kelvin --> 345 Kelvin No Conversion Required
Initial Temperature: 305 Kelvin --> 305 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: 0.1 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ηstirling = 100*((R*ln(r)*(Tf-Ti))/(R*Tf*ln(r)+Cv*(1-ϵ)*(Tf-Ti))) --> 100*((8.314*ln(1.75)*(345-305))/(8.314*345*ln(1.75)+100*(1-0.1)*(345-305)))
Evaluating ... ...
ηstirling = 3.57540840251781
STEP 3: Convert Result to Output's Unit
3.57540840251781 --> No Conversion Required
FINAL ANSWER
3.57540840251781 3.575408 <-- Thermal Efficiency of Stirling Cycle
(Calculation completed in 00.004 seconds)

Credits

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

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness
Go Thermal Efficiency of Stirling Cycle = 100*((Universal Gas Constant*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/(Universal Gas Constant*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature)))
Mean Effective Pressure in Dual Cycle
Go Mean Effective Pressure of Dual Cycle = Pressure at Start of Isentropic Compression*(Compression Ratio^Heat Capacity Ratio*((Explosion Ratio-1)+Heat Capacity Ratio*Explosion Ratio*(Cutoff Ratio-1))-Compression Ratio*(Explosion Ratio*Cutoff Ratio^Heat Capacity Ratio-1))/((Heat Capacity Ratio-1)*(Compression Ratio-1))
Work Output for Dual Cycle
Go Work Output of Engine = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*Pressure Ratio*(Cutoff Ratio-1)+(Pressure Ratio-1))-(Pressure Ratio*Cutoff Ratio^(Heat Capacity Ratio)-1))/(Heat Capacity Ratio-1)
Work Output for Diesel Cycle
Go Work Output of Engine = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*(Cutoff Ratio-1)-Compression Ratio^(1-Heat Capacity Ratio)*(Cutoff Ratio^(Heat Capacity Ratio)-1)))/(Heat Capacity Ratio-1)
Mean Effective Pressure in Diesel Cycle
Go Mean Effective Pressure in Diesel Cycle = Pressure at Start of Isentropic Compression*(Heat Capacity Ratio*Compression Ratio^Heat Capacity Ratio*(Cutoff Ratio-1)-Compression Ratio*(Cutoff 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))*((Explosion Ratio*Cutoff Ratio^Heat Capacity Ratio-1)/(Explosion Ratio-1+Explosion Ratio*Heat Capacity Ratio*(Cutoff Ratio-1))))
Mean Effective Pressure in Otto Cycle
Go Mean Effective Pressure = 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 Engine = 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)
Thermal Efficiency of Diesel Cycle
Go Thermal Efficiency of Diesel Cycle = 100*(1-1/Compression Ratio^(Heat Capacity Ratio-1)*(Cutoff Ratio^Heat Capacity Ratio-1)/(Heat Capacity Ratio*(Cutoff Ratio-1)))
Air Standard Efficiency for Diesel Engines
Go Air Standard Efficiency = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cutoff Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cutoff 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 Air Standard Efficiency = 100*(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 Air Standard Efficiency = Indicated Thermal Efficiency/Relative Efficiency
Thermal Efficiency of Otto Cycle
Go OTE = 1-1/Compression Ratio^(Heat Capacity Ratio-1)
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

Thermal Efficiency of Stirling Cycle = 100*((Universal Gas Constant*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/(Universal Gas Constant*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature)))
ηstirling = 100*((R*ln(r)*(Tf-Ti))/(R*Tf*ln(r)+Cv*(1-ϵ)*(Tf-Ti)))

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*((Universal Gas Constant*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/(Universal Gas Constant*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, The Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness formula is defined as the fraction of heat converted into useful work in an engine working on the Stirling cycle. It takes into account the compression ratio as well as heat exchanger effectiveness. Thermal Efficiency of Stirling Cycle is denoted by ηstirling 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 Universal Gas Constant (R), Compression Ratio (r), Final Temperature (Tf), Initial Temperature (Ti), Molar Specific Heat Capacity at Constant Volume (Cv) & 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 -> 3.575408 = 100*((8.314*ln(1.75)*(345-305))/(8.314*345*ln(1.75)+100*(1-0.1)*(345-305))).

FAQ

What is Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness?
The Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness formula is defined as the fraction of heat converted into useful work in an engine working on the Stirling cycle. It takes into account the compression ratio as well as heat exchanger effectiveness and is represented as ηstirling = 100*((R*ln(r)*(Tf-Ti))/(R*Tf*ln(r)+Cv*(1-ϵ)*(Tf-Ti))) or Thermal Efficiency of Stirling Cycle = 100*((Universal Gas Constant*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/(Universal Gas Constant*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature))). Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joule*kelvin−1*mole−1, Compression ratio is ratio between volume of cylinder and combustion chamber, Final Temperature is the measure of hotness or coldness of a system at its final state, Initial Temperature is the measure of hotness or coldness of a system at its initial state, Molar Specific Heat Capacity at Constant Volume , Cv ( of a gas ) is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant volume & The effectiveness of heat exchanger is defined as the ratio of the actual heat transfer to the maximum possible heat transfer.
How to calculate Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness?
The Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness formula is defined as the fraction of heat converted into useful work in an engine working on the Stirling cycle. It takes into account the compression ratio as well as heat exchanger effectiveness is calculated using Thermal Efficiency of Stirling Cycle = 100*((Universal Gas Constant*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/(Universal Gas Constant*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 Universal Gas Constant (R), Compression Ratio (r), Final Temperature (Tf), Initial Temperature (Ti), Molar Specific Heat Capacity at Constant Volume (Cv) & Effectiveness of Heat Exchanger (ϵ). With our tool, you need to enter the respective value for Universal Gas Constant, 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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!