Thermal Efficiency of Diesel Cycle Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
ηth = 100*(1-1/r^(γ-1)*(rc^γ-1)/(γ*(rc-1)))
This formula uses 4 Variables
Variables Used
Thermal Efficiency of Diesel Cycle - Thermal Efficiency of Diesel Cycle (in %) is the efficiency at which the heat is converted into useful work by an engine working on the diesel 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.
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
Compression Ratio: 1.75 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
Cutoff Ratio: 1.56 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ηth = 100*(1-1/r^(γ-1)*(rc^γ-1)/(γ*(rc-1))) --> 100*(1-1/1.75^(1.4-1)*(1.56^1.4-1)/(1.4*(1.56-1)))
Evaluating ... ...
ηth = 11.9299475409505
STEP 3: Convert Result to Output's Unit
11.9299475409505 --> No Conversion Required
FINAL ANSWER
11.9299475409505 11.92995 <-- Thermal Efficiency of Diesel Cycle
(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

Thermal Efficiency of Diesel Cycle Formula

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)))
ηth = 100*(1-1/r^(γ-1)*(rc^γ-1)/(γ*(rc-1)))

When is this formula valid?

This formula is valid under cold air standard analysis and gives the ideal thermal efficiency. The actual thermal efficiency will be significantly lower due to heat and friction losses.

What terms do the maximum thermal efficiency of Diesel cycle depend on?

The maximum thermal efficiency of a Diesel cycle is dependent on the compression ratio and the cut-off ratio.

How to Calculate Thermal Efficiency of Diesel Cycle?

Thermal Efficiency of Diesel Cycle calculator uses 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))) to calculate the Thermal Efficiency of Diesel Cycle, The Thermal Efficiency of Diesel Cycle formula can be defined as the amount of thermal energy converted into useful work during the diesel cycle. Thermal Efficiency of Diesel Cycle is denoted by ηth symbol.

How to calculate Thermal Efficiency of Diesel Cycle using this online calculator? To use this online calculator for Thermal Efficiency of Diesel Cycle, enter Compression Ratio (r), Heat Capacity Ratio (γ) & Cutoff Ratio (rc) and hit the calculate button. Here is how the Thermal Efficiency of Diesel Cycle calculation can be explained with given input values -> 11.92995 = 100*(1-1/1.75^(1.4-1)*(1.56^1.4-1)/(1.4*(1.56-1))).

FAQ

What is Thermal Efficiency of Diesel Cycle?
The Thermal Efficiency of Diesel Cycle formula can be defined as the amount of thermal energy converted into useful work during the diesel cycle and is represented as ηth = 100*(1-1/r^(γ-1)*(rc^γ-1)/(γ*(rc-1))) or 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))). 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 & Cutoff Ratio is the ratio of the volume after combustion to the volume before combustion.
How to calculate Thermal Efficiency of Diesel Cycle?
The Thermal Efficiency of Diesel Cycle formula can be defined as the amount of thermal energy converted into useful work during the diesel cycle is calculated using 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))). To calculate Thermal Efficiency of Diesel Cycle, you need Compression Ratio (r), Heat Capacity Ratio (γ) & Cutoff Ratio (rc). With our tool, you need to enter the respective value for Compression Ratio, Heat Capacity Ratio & Cutoff Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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