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Work Output for Otto Cycle Formula

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The work output of otto cycle is the net difference between the work done on the gas during compression and the work done by the gas during expansion. It is the area enclosed by p-v diagram. Check FAQs

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

W_o - Work Output of Otto Cycle?P₁ - Pressure at Start of Isentropic Compression?V₁ - Volume at Start of Isentropic Compression?r_p - Pressure Ratio?r - Compression Ratio?γ - Heat Capacity Ratio?

Work Output for Otto Cycle Example

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Here is how the Work Output for Otto Cycle equation looks like with Values.

Here is how the Work Output for Otto Cycle equation looks like with Units.

Here is how the Work Output for Otto Cycle equation looks like.

968.0783 = 110 \cdot 0.65 \cdot \frac{(3.34 - 1) \cdot (20^{1.4 - 1} - 1)}{1.4 - 1}

968.0783KJ = 110kPa \cdot 0.65m³ \cdot \frac{(3.34 - 1) \cdot (20^{1.4 - 1} - 1)}{1.4 - 1}

968.0783 = 110 \cdot 0.65 \cdot \frac{(3.34 - 1) \cdot (20^{1.4 - 1} - 1)}{1.4 - 1}

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Work Output for Otto Cycle Solution

Follow our step by step solution on how to calculate Work Output for Otto Cycle?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

W o = 110kPa \cdot 0.65m³ \cdot \frac{(3.34 - 1) \cdot (20^{1.4 - 1} - 1)}{1.4 - 1}

Next Step Convert Units

∴

W o = 110000Pa \cdot 0.65m³ \cdot \frac{(3.34 - 1) \cdot (20^{1.4 - 1} - 1)}{1.4 - 1}

Next Step Prepare to Evaluate

∴

W o = 110000 \cdot 0.65 \cdot \frac{(3.34 - 1) \cdot (20^{1.4 - 1} - 1)}{1.4 - 1}

Next Step Evaluate

∴

W o = 968078.254102883J

Next Step Convert to Output's Unit

∴

W o = 968.078254102883KJ

LAST Step Rounding Answer

∴

W o = 968.0783KJ

Work Output for Otto Cycle Formula Elements

Variables

Work Output of Otto Cycle

The work output of otto cycle is the net difference between the work done on the gas during compression and the work done by the gas during expansion. It is the area enclosed by p-v diagram.

Symbol: W_o

Measurement: EnergyUnit: KJ

Note: Value should be greater than 0.

Formulas to find Work Output of Otto Cycle

Pressure at Start of Isentropic Compression

Pressure at Start of Isentropic Compression refers to the pressure exerted by the charge inside the wall of the cylinder at the start of the reversible adiabatic compression process in IC engine.

Symbol: P₁

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Pressure at Start of Isentropic Compression

Volume at Start of Isentropic Compression

Volume at Start of Isentropic Compression is the volume of the engine cylinder before reversible adiabatic process, keeping entropy as constant. It is essentially the swept volume of the cylinder.

Symbol: V₁

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume at Start of Isentropic Compression

Pressure Ratio

Pressure ratio is the ratio of the maximum pressure during combustion to the minimum pressure at the end of exhaust, reflecting compression and expansion characteristics of the engine cycle.

Symbol: r_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Pressure 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

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

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 Diesel Cycle

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

How to Evaluate Work Output for Otto Cycle?

Work Output for Otto Cycle evaluator uses 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) to evaluate the Work Output of Otto Cycle, Work Output for Otto Cycle refers to the net mechanical work obtained by the petrol engine during the power stroke. This work is calculated as the area enclosed by the pressure-volume (P-V) diagram of the otto cycle. It represents the usable energy extracted from the fuel by the engine. It is a crucial parameter for determining the efficiency of the engine. Work Output of Otto Cycle is denoted by W_o symbol.

How to evaluate Work Output for Otto Cycle using this online evaluator? To use this online evaluator for Work Output for Otto Cycle, enter Pressure at Start of Isentropic Compression (P₁), Volume at Start of Isentropic Compression (V₁), Pressure Ratio (r_p), Compression Ratio (r) & Heat Capacity Ratio (γ) and hit the calculate button.

FAQs on Work Output for Otto Cycle

What is the formula to find Work Output for Otto Cycle?

The formula of Work Output for Otto Cycle is expressed as 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). Here is an example- 0.968078 = 110000*0.65*((3.34-1)*(20^(1.4-1)-1))/(1.4-1).

How to calculate Work Output for Otto Cycle?

With Pressure at Start of Isentropic Compression (P₁), Volume at Start of Isentropic Compression (V₁), Pressure Ratio (r_p), Compression Ratio (r) & Heat Capacity Ratio (γ) we can find Work Output for Otto Cycle using the formula - 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).

Can the Work Output for Otto Cycle be negative?

No, the Work Output for Otto Cycle, measured in Energy cannot be negative.

Which unit is used to measure Work Output for Otto Cycle?

Work Output for Otto Cycle is usually measured using the Kilojoule[KJ] for Energy. Joule[KJ], Gigajoule[KJ], Megajoule[KJ] are the few other units in which Work Output for Otto Cycle can be measured.

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Work Output for Otto Cycle Formula

Work Output for Otto Cycle Example

Work Output for Otto Cycle Solution

Work Output for Otto Cycle Formula Elements

Other formulas in Air Standard Cycles category

How to Evaluate Work Output for Otto Cycle?

FAQs on Work Output for Otto Cycle

Variable Name