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Thermal Efficiency of Diesel Cycle Formula

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The Thermal Efficiency of Diesel Cycle represents the effectiveness of Diesel 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 th = 1 - \frac{1}{r^{γ - 1}} \cdot \frac{{r c}^{γ} - 1}{γ \cdot (r c - 1)}

η_th - Thermal Efficiency of Diesel Cycle?r - Compression Ratio?γ - Heat Capacity Ratio?r_c - Cut-off Ratio?

Thermal Efficiency of Diesel Cycle Example

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

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

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

0.649 = 1 - \frac{1}{20^{1.4 - 1}} \cdot \frac{{1.95}^{1.4} - 1}{1.4 \cdot (1.95 - 1)}

0.649 = 1 - \frac{1}{20^{1.4 - 1}} \cdot \frac{{1.95}^{1.4} - 1}{1.4 \cdot (1.95 - 1)}

0.649 = 1 - \frac{1}{20^{1.4 - 1}} \cdot \frac{{1.95}^{1.4} - 1}{1.4 \cdot (1.95 - 1)}

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Thermal Efficiency of Diesel Cycle Solution

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

FIRST Step Consider the formula

η th = 1 - \frac{1}{r^{γ - 1}} \cdot \frac{{r c}^{γ} - 1}{γ \cdot (r c - 1)}

Next Step Substitute values of Variables

∴

η th = 1 - \frac{1}{20^{1.4 - 1}} \cdot \frac{{1.95}^{1.4} - 1}{1.4 \cdot (1.95 - 1)}

Next Step Prepare to Evaluate

∴

η th = 1 - \frac{1}{20^{1.4 - 1}} \cdot \frac{{1.95}^{1.4} - 1}{1.4 \cdot (1.95 - 1)}

Next Step Evaluate

∴

η th = 0.649039049927023

LAST Step Rounding Answer

∴

η th = 0.649

Thermal Efficiency of Diesel Cycle Formula Elements

Variables

Thermal Efficiency of Diesel Cycle

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

Symbol: η_th

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Thermal Efficiency of Diesel Cycle

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

Cut-off Ratio

Cut-off ratio is the ratio of the cylinder volume at the start of compression stroke to the volume at the end of expansion stroke. It's a measure of piston's compression of the charge before ignition.

Symbol: r_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cut-off 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 Diesel Cycle?

Thermal Efficiency of Diesel Cycle evaluator uses Thermal Efficiency of Diesel Cycle = 1-1/Compression Ratio^(Heat Capacity Ratio-1)*(Cut-off Ratio^Heat Capacity Ratio-1)/(Heat Capacity Ratio*(Cut-off Ratio-1)) to evaluate the Thermal Efficiency of Diesel Cycle, The thermal efficiency of Diesel cycle measures how efficiently a diesel engine converts heat energy from fuel into mechanical work. It reflects the effectiveness of converting heat from burning fuel into usable work output at crankshaft. Diesel engines achieve ignition through high compression, eliminating the need for spark plugs, but this high compression results in some theoretical efficiency loss compared to gasoline engines using the Otto cycle. Thermal Efficiency of Diesel Cycle is denoted by η_th symbol.

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

FAQs on Thermal Efficiency of Diesel Cycle

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

The formula of Thermal Efficiency of Diesel Cycle is expressed as Thermal Efficiency of Diesel Cycle = 1-1/Compression Ratio^(Heat Capacity Ratio-1)*(Cut-off Ratio^Heat Capacity Ratio-1)/(Heat Capacity Ratio*(Cut-off Ratio-1)). Here is an example- 0.649039 = 1-1/20^(1.4-1)*(1.95^1.4-1)/(1.4*(1.95-1)).

How to calculate Thermal Efficiency of Diesel Cycle?

With Compression Ratio (r), Heat Capacity Ratio (γ) & Cut-off Ratio (r_c) we can find Thermal Efficiency of Diesel Cycle using the formula - Thermal Efficiency of Diesel Cycle = 1-1/Compression Ratio^(Heat Capacity Ratio-1)*(Cut-off Ratio^Heat Capacity Ratio-1)/(Heat Capacity Ratio*(Cut-off Ratio-1)).

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Thermal Efficiency of Diesel Cycle Formula

Thermal Efficiency of Diesel Cycle Example

Thermal Efficiency of Diesel Cycle Solution

Thermal Efficiency of Diesel Cycle Formula Elements

Other formulas in Air Standard Cycles category

How to Evaluate Thermal Efficiency of Diesel Cycle?

FAQs on Thermal Efficiency of Diesel Cycle

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