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Thermal Efficiency of Atkinson Cycle Formula

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The Thermal Efficiency of Atkinson Cycle represents the effectiveness of Atkinson engine. It is measured by comparing how much work is done through out the system to the heat supplied to the system. Check FAQs

η a = 100 \cdot (1 - γ \cdot (\frac{e - r}{e^{γ} - r^{γ}}))

η_a - Thermal Efficiency of Atkinson Cycle?γ - Heat Capacity Ratio?e - Expansion Ratio?r - Compression Ratio?

Thermal Efficiency of Atkinson Cycle Example

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Here is how the Thermal Efficiency of Atkinson Cycle equation looks like with Values.

Here is how the Thermal Efficiency of Atkinson Cycle equation looks like with Units.

Here is how the Thermal Efficiency of Atkinson Cycle equation looks like.

62.2417 = 100 \cdot (1 - 1.4 \cdot (\frac{4 - 20}{4^{1.4} - 20^{1.4}}))

62.2417 = 100 \cdot (1 - 1.4 \cdot (\frac{4 - 20}{4^{1.4} - 20^{1.4}}))

62.2417 = 100 \cdot (1 - 1.4 \cdot (\frac{4 - 20}{4^{1.4} - 20^{1.4}}))

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Thermal Efficiency of Atkinson Cycle Solution

Follow our step by step solution on how to calculate Thermal Efficiency of Atkinson Cycle?

FIRST Step Consider the formula

η a = 100 \cdot (1 - γ \cdot (\frac{e - r}{e^{γ} - r^{γ}}))

Next Step Substitute values of Variables

∴

η a = 100 \cdot (1 - 1.4 \cdot (\frac{4 - 20}{4^{1.4} - 20^{1.4}}))

Next Step Prepare to Evaluate

∴

η a = 100 \cdot (1 - 1.4 \cdot (\frac{4 - 20}{4^{1.4} - 20^{1.4}}))

Next Step Evaluate

∴

η a = 62.2416815892081

LAST Step Rounding Answer

∴

η a = 62.2417

Thermal Efficiency of Atkinson Cycle Formula Elements

Variables

Thermal Efficiency of Atkinson Cycle

The Thermal Efficiency of Atkinson Cycle represents the effectiveness of Atkinson engine. It is measured by comparing how much work is done through out the system to the heat supplied to the system.

Symbol: η_a

Measurement: NAUnit: Unitless

Note: Value should be less than 100.

Formulas to find Thermal Efficiency of Atkinson Cycle

Heat Capacity Ratio

The Heat Capacity Ratio or, adiabatic index quantifies the relationship between heat added at constant pressure and the resulting temperature increase compared to heat added at constant volume.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Heat Capacity Ratio

Expansion Ratio

Expansion ratio is the ratio of cylinder volume after compression (highest pressure) to volume at exhaust (lowest pressure).

Symbol: e

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Expansion Ratio

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.

Symbol: r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Compression Ratio

Other formulas in Air Standard Cycles category

Go Mean Effective Pressure in Otto Cycle

P O = P 1 \cdot r \cdot (\frac{(r^{γ - 1} - 1) \cdot (r p - 1)}{(r - 1) \cdot (γ - 1)})

Go Mean Effective Pressure in Diesel Cycle

P D = P 1 \cdot \frac{γ \cdot r^{γ} \cdot (r c - 1) - r \cdot ({r c}^{γ} - 1)}{(γ - 1) \cdot (r - 1)}

Go Mean Effective Pressure in Dual Cycle

P d = P 1 \cdot \frac{r^{γ} \cdot ((R p - 1) + γ \cdot R p \cdot (r c - 1)) - r \cdot (R p \cdot {r c}^{γ} - 1)}{(γ - 1) \cdot (r - 1)}

Go Work Output for Otto Cycle

W o = P 1 \cdot V 1 \cdot \frac{(r p - 1) \cdot (r^{γ - 1} - 1)}{γ - 1}

How to Evaluate Thermal Efficiency of Atkinson Cycle?

Thermal Efficiency of Atkinson Cycle evaluator uses Thermal Efficiency of Atkinson Cycle = 100*(1-Heat Capacity Ratio*((Expansion Ratio-Compression Ratio)/(Expansion Ratio^(Heat Capacity Ratio)-Compression Ratio^(Heat Capacity Ratio)))) to evaluate the Thermal Efficiency of Atkinson Cycle, Thermal Efficiency of Atkinson Cycle refers to the effectiveness of Atkinson engine to convert heat energy from burning fuel into usable work output. Atkinson cycle engines prioritize a longer expansion stroke compared to a traditional Otto cycle. This theoretically allows for more complete extraction of thermal energy, potentially leading to higher efficiency. However, achieving this theoretical advantage in real-world engines requires balancing efficiency gains with power output. Thermal Efficiency of Atkinson Cycle is denoted by η_a symbol.

How to evaluate Thermal Efficiency of Atkinson Cycle using this online evaluator? To use this online evaluator for Thermal Efficiency of Atkinson Cycle, enter Heat Capacity Ratio (γ), Expansion Ratio (e) & Compression Ratio (r) and hit the calculate button.

FAQs on Thermal Efficiency of Atkinson Cycle

What is the formula to find Thermal Efficiency of Atkinson Cycle?

The formula of Thermal Efficiency of Atkinson Cycle is expressed as Thermal Efficiency of Atkinson Cycle = 100*(1-Heat Capacity Ratio*((Expansion Ratio-Compression Ratio)/(Expansion Ratio^(Heat Capacity Ratio)-Compression Ratio^(Heat Capacity Ratio)))). Here is an example- 62.24168 = 100*(1-1.4*((4-20)/(4^(1.4)-20^(1.4)))).

How to calculate Thermal Efficiency of Atkinson Cycle?

With Heat Capacity Ratio (γ), Expansion Ratio (e) & Compression Ratio (r) we can find Thermal Efficiency of Atkinson Cycle using the formula - Thermal Efficiency of Atkinson Cycle = 100*(1-Heat Capacity Ratio*((Expansion Ratio-Compression Ratio)/(Expansion Ratio^(Heat Capacity Ratio)-Compression Ratio^(Heat Capacity Ratio)))).

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Thermal Efficiency of Atkinson Cycle Formula

Thermal Efficiency of Atkinson Cycle Example

Thermal Efficiency of Atkinson Cycle Solution

Thermal Efficiency of Atkinson Cycle Formula Elements

Other formulas in Air Standard Cycles category

How to Evaluate Thermal Efficiency of Atkinson Cycle?

FAQs on Thermal Efficiency of Atkinson Cycle

Variable Name