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Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness Formula

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The Thermal Efficiency of Stirling Cycle represents the effectiveness of Stirling 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 s = 100 \cdot (\frac{[R] \cdot \ln (r) \cdot (T f - T i)}{[R] \cdot T f \cdot \ln (r) + C v \cdot (1 - ε) \cdot (T f - T i)})

η_s - Thermal Efficiency of Stirling Cycle?r - Compression Ratio?T_f - Final Temperature?T_i - Initial Temperature?C_v - Molar Specific Heat Capacity at Constant Volume?ε - Effectiveness of Heat Exchanger?[R] - Universal gas constant?[R] - Universal gas constant?

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness Example

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Here is how the Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness equation looks like with Values.

Here is how the Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness equation looks like with Units.

Here is how the Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness equation looks like.

19.8854 = 100 \cdot (\frac{8.3145 \cdot \ln (20) \cdot (423 - 283)}{8.3145 \cdot 423 \cdot \ln (20) + 100 \cdot (1 - 0.5) \cdot (423 - 283)})

19.8854 = 100 \cdot (\frac{8.3145 \cdot \ln (20) \cdot (423K - 283K)}{8.3145 \cdot 423K \cdot \ln (20) + 100J/K*mol \cdot (1 - 0.5) \cdot (423K - 283K)})

19.8854 = 100 \cdot (\frac{8.3145 \cdot \ln (20) \cdot (423 - 283)}{8.3145 \cdot 423 \cdot \ln (20) + 100 \cdot (1 - 0.5) \cdot (423 - 283)})

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Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness Solution

Follow our step by step solution on how to calculate Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness?

FIRST Step Consider the formula

η s = 100 \cdot (\frac{[R] \cdot \ln (r) \cdot (T f - T i)}{[R] \cdot T f \cdot \ln (r) + C v \cdot (1 - ε) \cdot (T f - T i)})

Next Step Substitute values of Variables

∴

η s = 100 \cdot (\frac{[R] \cdot \ln (20) \cdot (423K - 283K)}{[R] \cdot 423K \cdot \ln (20) + 100J/K*mol \cdot (1 - 0.5) \cdot (423K - 283K)})

Next Step Substitute values of Constants

∴

η s = 100 \cdot (\frac{8.3145 \cdot \ln (20) \cdot (423K - 283K)}{8.3145 \cdot 423K \cdot \ln (20) + 100J/K*mol \cdot (1 - 0.5) \cdot (423K - 283K)})

Next Step Prepare to Evaluate

∴

η s = 100 \cdot (\frac{8.3145 \cdot \ln (20) \cdot (423 - 283)}{8.3145 \cdot 423 \cdot \ln (20) + 100 \cdot (1 - 0.5) \cdot (423 - 283)})

Next Step Evaluate

∴

η s = 19.8853668537813

LAST Step Rounding Answer

∴

η s = 19.8854

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness Formula Elements

Variables

Constants

Functions

Thermal Efficiency of Stirling Cycle

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

Symbol: η_s

Measurement: NAUnit: Unitless

Note: Value should be less than 100.

Formulas to find Thermal Efficiency of Stirling 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

Final Temperature

Final Temperature can be referred as the temperature of cylinder after ignition or final temperature of the charge before work is extracted. It is measured in absolute temperature (kelvin-scale).

Symbol: T_f

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Final Temperature

Initial Temperature

Initial Temperature can be referred as the temperature of cylinder after intake stroke or initial temperature of the charge. It is measured in absolute temperature (Kelvin-scale).

Symbol: T_i

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Initial Temperature

Molar Specific Heat Capacity at Constant Volume

Molar Specific Heat Capacity at Constant Volume is the amount of heat required to raise the temperature of one mol of the gas by one degree at constant volume.

Symbol: C_v

Measurement: Molar Specific Heat Capacity at Constant VolumeUnit: J/K*mol

Note: Value should be greater than 0.

Formulas to find Molar Specific Heat Capacity at Constant Volume

Effectiveness of Heat Exchanger

The effectiveness of heat exchanger is a ratio of actual heat transfer to the maximum possible transfer in ideal scenario. It reflects how well a device extracts heat from higher to lower sink.

Symbol: ε

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Effectiveness of Heat Exchanger

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

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 Stirling Cycle given Heat Exchanger Effectiveness?

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness evaluator uses Thermal Efficiency of Stirling Cycle = 100*(([R]*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/([R]*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature))) to evaluate the Thermal Efficiency of Stirling Cycle, Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness refers to how effectively a Stirling 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. It takes into account the compression ratio as well as heat exchanger effectiveness. Thermal Efficiency of Stirling Cycle is denoted by η_s symbol.

How to evaluate Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness using this online evaluator? To use this online evaluator for Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness, enter Compression Ratio (r), Final Temperature (T_f), Initial Temperature (T_i), Molar Specific Heat Capacity at Constant Volume (C_v) & Effectiveness of Heat Exchanger (ε) and hit the calculate button.

FAQs on Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness

What is the formula to find Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness?

The formula of Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness is expressed as Thermal Efficiency of Stirling Cycle = 100*(([R]*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/([R]*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature))). Here is an example- 19.88537 = 100*(([R]*ln(20)*(423-283))/([R]*423*ln(20)+100*(1-0.5)*(423-283))).

How to calculate Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness?

With Compression Ratio (r), Final Temperature (T_f), Initial Temperature (T_i), Molar Specific Heat Capacity at Constant Volume (C_v) & Effectiveness of Heat Exchanger (ε) we can find Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness using the formula - Thermal Efficiency of Stirling Cycle = 100*(([R]*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/([R]*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature))). This formula also uses Universal gas constant, Universal gas constant and Natural Logarithm (ln) function(s).

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Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness Formula

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness Example

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness Solution

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness Formula Elements

Other formulas in Air Standard Cycles category

How to Evaluate Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness?

FAQs on Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness

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