Work Output for Dual Cycle Calculator

⤿

✖Pressure at Start of Isentropic Compression is the pressure inside the piston cylinder at the start of the isentropic compression process in an otto cycle.ⓘ Pressure at Start of Isentropic Compression [P₁]			+10% -10%
✖Volume at Start of Isentropic Compression is the volume of the engine cylinder at the start of isentropic compression process, i.e. initial volume, in an air-standard cycle.ⓘ Volume at Start of Isentropic Compression [V₁]			+10% -10%
✖Compression ratio is ratio of volume of cylinder to volume combustion chamber.ⓘ Compression Ratio [r]			+10% -10%
✖The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heat at constant pressure to specific heat at constant volume of air.ⓘ Heat Capacity Ratio [γ]			+10% -10%
✖Pressure ratio is the ratio of final to initial pressure inside bore of the engine.ⓘ Pressure Ratio [r_p]			+10% -10%
✖Cut-off ratio is the ratio of the volume of combustion chamber after combustion to the volume of combustion chamber before combustion.ⓘ Cut-off Ratio [r_c]			+10% -10%

✖The work output of dual cycle, can be referred as the net work done by the dual cycle engine upon given heat energy as input.ⓘ Work Output for Dual Cycle [W_dual]

⎘ Copy

👎

Formula

✖

Work Output for Dual Cycle

Formula

`"W"_{"dual"} = "P"_{"1"}*"V"_{"1"}*("r"^("γ"-1)*("γ"*"r"_{"p"}*("r"_{"c"}-1)+("r"_{"p"}-1))-("r"_{"p"}*"r"_{"c"}^("γ")-1))/("γ"-1)`

Example

`"2676.232KJ"="110kPa"*"0.65m³"*(("20")^("1.4"-1)*("1.4"*"3.34"*("1.95"-1)+("3.34"-1))-("3.34"*("1.95")^("1.4")-1))/("1.4"-1)`

Calculator

LaTeX

Reset

👍

Download Air-Standard Cycles Formulas PDF PDF Image

Work Output for Dual Cycle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
W_dual = P₁*V₁*(r^(γ-1)*(γ*r_p*(r_c-1)+(r_p-1))-(r_p*r_c^(γ)-1))/(γ-1)
This formula uses 7 Variables

Variables Used

Work Output of Dual Cycle - (Measured in Joule) - The work output of dual cycle, can be referred as the net work done by the dual cycle engine upon given heat energy as input.
Pressure at Start of Isentropic Compression - (Measured in Pascal) - Pressure at Start of Isentropic Compression is the pressure inside the piston cylinder at the start of the isentropic compression process in an otto cycle.
Volume at Start of Isentropic Compression - (Measured in Cubic Meter) - Volume at Start of Isentropic Compression is the volume of the engine cylinder at the start of isentropic compression process, i.e. initial volume, in an air-standard cycle.
Compression Ratio - Compression ratio is ratio of volume of cylinder to volume combustion chamber.
Heat Capacity Ratio - The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heat at constant pressure to specific heat at constant volume of air.
Pressure Ratio - Pressure ratio is the ratio of final to initial pressure inside bore of the engine.
Cut-off Ratio - Cut-off ratio is the ratio of the volume of combustion chamber after combustion to the volume of combustion chamber before combustion.

STEP 1: Convert Input(s) to Base Unit

Pressure at Start of Isentropic Compression: 110 Kilopascal --> 110000 Pascal (Check conversion here)
Volume at Start of Isentropic Compression: 0.65 Cubic Meter --> 0.65 Cubic Meter No Conversion Required
Compression Ratio: 20 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
Pressure Ratio: 3.34 --> No Conversion Required
Cut-off Ratio: 1.95 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_dual = P₁*V₁*(r^(γ-1)*(γ*r_p*(r_c-1)+(r_p-1))-(r_p*r_c^(γ)-1))/(γ-1) --> 110000*0.65*(20^(1.4-1)*(1.4*3.34*(1.95-1)+(3.34-1))-(3.34*1.95^(1.4)-1))/(1.4-1)

Evaluating ... ...

W_dual = 2676232.10257339

STEP 3: Convert Result to Output's Unit

2676232.10257339 Joule -->2676.23210257339 Kilojoule (Check conversion here)

FINAL ANSWER

2676.23210257339 ≈ 2676.232 Kilojoule <-- Work Output of Dual Cycle

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » IC Engine » Air-Standard Cycles » Work Output for Dual Cycle

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))/(Universal Gas Constant*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 Air Standard 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 = 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 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 of Otto Cycle = 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

Work Output for Dual Cycle Formula

What is Dual Cycle?

Dual cycle or Limited Pressure cycle is a thermodynamic cycle that combines the Otto cycle and the Diesel cycle. In the dual cycle, combustion occurs partly at constant volume and partly at constant pressure.
In a dual cycle, the system executing the cycle undergoes a series of five processes: two isentropic (reversible adiabatic) processes alternated with two isochoric processes and one isobaric process.

How to Calculate Work Output for Dual Cycle?

Work Output for Dual Cycle calculator uses 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) to calculate the Work Output of Dual Cycle, The Work Output for Dual Cycle formula is defined as the thermodynamic work done by a heat engine working on a Dual cycle, in which case the amount of work output must be less than the input as energy is lost to heat. Work Output of Dual Cycle is denoted by W_dual symbol.

How to calculate Work Output for Dual Cycle using this online calculator? To use this online calculator for Work Output for Dual Cycle, enter Pressure at Start of Isentropic Compression (P₁), Volume at Start of Isentropic Compression (V₁), Compression Ratio (r), Heat Capacity Ratio (γ), Pressure Ratio (r_p) & Cut-off Ratio (r_c) and hit the calculate button. Here is how the Work Output for Dual Cycle calculation can be explained with given input values -> 2.676232 = 110000*0.65*(20^(1.4-1)*(1.4*3.34*(1.95-1)+(3.34-1))-(3.34*1.95^(1.4)-1))/(1.4-1).

FAQ

What is Work Output for Dual Cycle?

The Work Output for Dual Cycle formula is defined as the thermodynamic work done by a heat engine working on a Dual cycle, in which case the amount of work output must be less than the input as energy is lost to heat and is represented as W_dual = P₁*V₁*(r^(γ-1)*(γ*r_p*(r_c-1)+(r_p-1))-(r_p*r_c^(γ)-1))/(γ-1) or 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). Pressure at Start of Isentropic Compression is the pressure inside the piston cylinder at the start of the isentropic compression process in an otto cycle, Volume at Start of Isentropic Compression is the volume of the engine cylinder at the start of isentropic compression process, i.e. initial volume, in an air-standard cycle, Compression ratio is ratio of volume of cylinder to volume combustion chamber, The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heat at constant pressure to specific heat at constant volume of air, Pressure ratio is the ratio of final to initial pressure inside bore of the engine & Cut-off ratio is the ratio of the volume of combustion chamber after combustion to the volume of combustion chamber before combustion.

How to calculate Work Output for Dual Cycle?

The Work Output for Dual Cycle formula is defined as the thermodynamic work done by a heat engine working on a Dual cycle, in which case the amount of work output must be less than the input as energy is lost to heat is calculated using 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). To calculate Work Output for Dual Cycle, you need Pressure at Start of Isentropic Compression (P₁), Volume at Start of Isentropic Compression (V₁), Compression Ratio (r), Heat Capacity Ratio (γ), Pressure Ratio (r_p) & Cut-off Ratio (r_c). With our tool, you need to enter the respective value for Pressure at Start of Isentropic Compression, Volume at Start of Isentropic Compression, Compression Ratio, Heat Capacity Ratio, Pressure Ratio & Cut-off Ratio 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