Maximum Electron Current per Unit Area Calculator

✖Emission Constant is a constant. An emission constant is a numerical value or coefficient used in mathematical equations .ⓘ Emission Constant [A]			+10% -10%
✖Temperature is a physical quantity that describes the level of thermal energy in a system.ⓘ Temperature [T]			+10% -10%
✖Work Function is a measure of the minimum amount of energy needed to remove an electron from a solid surface and set it free.ⓘ Work Function [Φ]			+10% -10%

✖Current Density is a measure of the flow of electric charge through a given area of a conductor.ⓘ Maximum Electron Current per Unit Area [J]

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Maximum Electron Current per Unit Area

Formula

`"J" = "A"*"T"^2*exp(-"Φ"/("[BoltZ]"*"T"))`

Example

`"3.138127A/cm²"="120"*("1100K")^2*exp(-"0.8eV"/("[BoltZ]"*"1100K"))`

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Maximum Electron Current per Unit Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Current Density = Emission Constant*Temperature^2*exp(-Work Function/([BoltZ]*Temperature))
J = A*T^2*exp(-Φ/([BoltZ]*T))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Current Density - (Measured in Ampere per Square Meter) - Current Density is a measure of the flow of electric charge through a given area of a conductor.
Emission Constant - Emission Constant is a constant. An emission constant is a numerical value or coefficient used in mathematical equations .
Temperature - (Measured in Kelvin) - Temperature is a physical quantity that describes the level of thermal energy in a system.
Work Function - (Measured in Joule) - Work Function is a measure of the minimum amount of energy needed to remove an electron from a solid surface and set it free.

STEP 1: Convert Input(s) to Base Unit

Emission Constant: 120 --> No Conversion Required
Temperature: 1100 Kelvin --> 1100 Kelvin No Conversion Required
Work Function: 0.8 Electron-Volt --> 1.28174186400001E-19 Joule (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = A*T^2*exp(-Φ/([BoltZ]*T)) --> 120*1100^2*exp(-1.28174186400001E-19/([BoltZ]*1100))

Evaluating ... ...

J = 31381.2706241948

STEP 3: Convert Result to Output's Unit

31381.2706241948 Ampere per Square Meter -->3.13812706241948 Ampere per Square Centimeter (Check conversion here)

FINAL ANSWER

3.13812706241948 ≈ 3.138127 Ampere per Square Centimeter <-- Current Density

(Calculation completed in 00.020 seconds)

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Created by Nisarg

Indian Institute of Technology,Roorlee (IITR), Roorkee

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< 12 Thermal Power Plant Calculators

Current Density from Cathode to Anode

Go Cathode Current Density = Emission Constant*Cathode Temperature^2*exp(-([Charge-e]*Cathode Voltage)/([BoltZ]*Cathode Temperature))

Maximum Electron Current per Unit Area

Go Current Density = Emission Constant*Temperature^2*exp(-Work Function/([BoltZ]*Temperature))

Net Kinetic Energy of Electron

Go Electron Net Energy = Cathode Current Density*((2*[BoltZ]*Cathode Temperature)/[Charge-e])

Output Voltage given Fermi Energy Levels

Go Output Voltage = (Anode Fermi Energy Level-Cathode Fermi Energy Level)/[Charge-e]

Power Output from Generator

Go Power Output = Output Voltage*(Cathode Current Density-Anode Current Density)

Consumption of Coal per Hour

Go Consumption of Coal per Hour = Heat Input per Hour/Calorific Value of Coal

Overall Efficiency of Power Station

Go Overall Efficiency = Thermal Efficiency*Electrical Efficiency

Thermal Efficiency of Power Station

Go Thermal Efficiency = Overall Efficiency/Electrical Efficiency

Output Voltage given Anode and Cathode Work Functions

Go Output Voltage = Cathode Work Function-Anode Work Function

Rankine Cycle Efficiency

Go Rankine Cycle Efficiency = Net Work Output/Heat Supplied

Minimum Energy required by Electron to Leave Cathode

Go Net Energy = Cathode Current Density*Cathode Voltage

Output Voltage given Anode and Cathode Voltages

Go Output Voltage = Cathode Voltage-Anode Voltage

Maximum Electron Current per Unit Area Formula

Current Density = Emission Constant*Temperature^2*exp(-Work Function/([BoltZ]*Temperature))
J = A*T^2*exp(-Φ/([BoltZ]*T))

What is the maximum power output of thermionic generator?

A single TEG generates power from 1 to 125 W. The use of more TEGs in a modular connection may increase the power up to 5 kW and Δ T max could be bigger than 70°C. Heat source , for example, a heat pipe system (the TEG devices and the heat pipe system can be used together in waste heat recovery systems).

How to Calculate Maximum Electron Current per Unit Area?

Maximum Electron Current per Unit Area calculator uses Current Density = Emission Constant*Temperature^2*exp(-Work Function/([BoltZ]*Temperature)) to calculate the Current Density, The Maximum Electron Current per Unit Area formula is defined as a measure of the flow of electric charge through a given area of a conductor. It is defined as the amount of electric current passing through a unit area perpendicular to the direction of current flow. Current Density is denoted by J symbol.

How to calculate Maximum Electron Current per Unit Area using this online calculator? To use this online calculator for Maximum Electron Current per Unit Area, enter Emission Constant (A), Temperature (T) & Work Function (Φ) and hit the calculate button. Here is how the Maximum Electron Current per Unit Area calculation can be explained with given input values -> 0.000314 = 120*1100^2*exp(-1.28174186400001E-19/([BoltZ]*1100)).

FAQ

What is Maximum Electron Current per Unit Area?

The Maximum Electron Current per Unit Area formula is defined as a measure of the flow of electric charge through a given area of a conductor. It is defined as the amount of electric current passing through a unit area perpendicular to the direction of current flow and is represented as J = A*T^2*exp(-Φ/([BoltZ]*T)) or Current Density = Emission Constant*Temperature^2*exp(-Work Function/([BoltZ]*Temperature)). Emission Constant is a constant. An emission constant is a numerical value or coefficient used in mathematical equations , Temperature is a physical quantity that describes the level of thermal energy in a system & Work Function is a measure of the minimum amount of energy needed to remove an electron from a solid surface and set it free.

How to calculate Maximum Electron Current per Unit Area?

The Maximum Electron Current per Unit Area formula is defined as a measure of the flow of electric charge through a given area of a conductor. It is defined as the amount of electric current passing through a unit area perpendicular to the direction of current flow is calculated using Current Density = Emission Constant*Temperature^2*exp(-Work Function/([BoltZ]*Temperature)). To calculate Maximum Electron Current per Unit Area, you need Emission Constant (A), Temperature (T) & Work Function (Φ). With our tool, you need to enter the respective value for Emission Constant, Temperature & Work Function 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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