Work Output for Dual Cycle Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
We = P1*V1*(r^(γ-1)*(γ*rp*(rc-1)+(rp-1))-(rp*rc^(γ)-1))/(γ-1)
This formula uses 7 Variables
Variables Used
Work Output of Engine - (Measured in Joule) - The Work Output of Engine refers to the thermodynamic work done by a heat engine, in which case the amount of work output must be less than the input as energy is lost to heat.
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 between volume of cylinder and combustion chamber.
Heat Capacity Ratio - The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Pressure Ratio - Pressure Ratio is ratio of final to initial pressure.
Cutoff Ratio - Cutoff Ratio is the ratio of the volume after combustion to the volume 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: 1.75 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
Pressure Ratio: 5.5 --> No Conversion Required
Cutoff Ratio: 1.56 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
We = P1*V1*(r^(γ-1)*(γ*rp*(rc-1)+(rp-1))-(rp*rc^(γ)-1))/(γ-1) --> 110000*0.65*(1.75^(1.4-1)*(1.4*5.5*(1.56-1)+(5.5-1))-(5.5*1.56^(1.4)-1))/(1.4-1)
Evaluating ... ...
We = 316821.980742813
STEP 3: Convert Result to Output's Unit
316821.980742813 Joule -->316.821980742813 Kilojoule (Check conversion here)
FINAL ANSWER
316.821980742813 316.822 Kilojoule <-- Work Output of Engine
(Calculation completed in 00.004 seconds)

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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

Work Output for Dual Cycle Formula

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)
We = P1*V1*(r^(γ-1)*(γ*rp*(rc-1)+(rp-1))-(rp*rc^(γ)-1))/(γ-1)

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 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) to calculate the Work Output of Engine, 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 Engine is denoted by We 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 (rp) & Cutoff Ratio (rc) and hit the calculate button. Here is how the Work Output for Dual Cycle calculation can be explained with given input values -> 0.316822 = 110000*0.65*(1.75^(1.4-1)*(1.4*5.5*(1.56-1)+(5.5-1))-(5.5*1.56^(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 We = P1*V1*(r^(γ-1)*(γ*rp*(rc-1)+(rp-1))-(rp*rc^(γ)-1))/(γ-1) or 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). 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 between volume of cylinder and combustion chamber, The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume, Pressure Ratio is ratio of final to initial pressure & Cutoff Ratio is the ratio of the volume after combustion to the volume 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 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). 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 (rp) & Cutoff Ratio (rc). 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 & Cutoff Ratio 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 Work Output of Engine?
In this formula, Work Output of Engine uses Pressure at Start of Isentropic Compression, Volume at Start of Isentropic Compression, Compression Ratio, Heat Capacity Ratio, Pressure Ratio & Cutoff Ratio. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • 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)
  • 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)
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