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Net Rate of Energy Supply to Cathode Calculator

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✖Cathode Current Density is a measure of the flow of electric charge through a given area of a conductor from Cathode.ⓘ Cathode Current Density [Jc]
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✖Cathode Voltage is the cathode potential.ⓘ Cathode Voltage [Vc]
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✖Cathode Temperature is a physical quantity that describes the level of thermal energy in a system, or the degree of hotness or coldness of Cathode.ⓘ Cathode Temperature [Tc]
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✖Anode Current Density is a measure of the flow of electric charge through a given area of a conductor from Anode.ⓘ Anode Current Density [Ja]
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✖Anode Voltage is the anode potential.ⓘ Anode Voltage [Va]
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✖Anode Temperature is a physical quantity that describes the level of thermal energy in a system, or the degree of hotness or coldness of Anode.ⓘ Anode Temperature [Ta]
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✖Cathode Net Energy is the total energy supplied to the cathode.ⓘ Net Rate of Energy Supply to Cathode [Qc]
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Formula
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Net Rate of Energy Supply to Cathode

Formula
`"Q"_{"c"} = "J"_{"c"}*("V"_{"c"}+(2*"[BoltZ]"*"T"_{"c"})/"[Charge-e]")-"J"_{"a"}*("V"_{"a"}+(2*"[BoltZ]"*"T"_{"a"})/"[Charge-e]")`

Example
`"0.395003W/cm²"="0.47A/cm²"*("1.25V"+(2*"[BoltZ]"*"1350K")/"[Charge-e]")-"0.26A/cm²"*("0.98V"+(2*"[BoltZ]"*"1050K")/"[Charge-e]")`

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Net Rate of Energy Supply to Cathode Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cathode Net Energy = Cathode Current Density*(Cathode Voltage+(2*[BoltZ]*Cathode Temperature)/[Charge-e])-Anode Current Density*(Anode Voltage+(2*[BoltZ]*Anode Temperature)/[Charge-e])
Qc = Jc*(Vc+(2*[BoltZ]*Tc)/[Charge-e])-Ja*(Va+(2*[BoltZ]*Ta)/[Charge-e])
This formula uses 2 Constants, 7 Variables
Constants Used
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19 Coulomb
[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23 Joule/Kelvin
Variables Used
Cathode Net Energy - (Measured in Watt per Square Meter) - Cathode Net Energy is the total energy supplied to the cathode.
Cathode Current Density - (Measured in Ampere per Square Meter) - Cathode Current Density is a measure of the flow of electric charge through a given area of a conductor from Cathode.
Cathode Voltage - (Measured in Volt) - Cathode Voltage is the cathode potential.
Cathode Temperature - (Measured in Kelvin) - Cathode Temperature is a physical quantity that describes the level of thermal energy in a system, or the degree of hotness or coldness of Cathode.
Anode Current Density - (Measured in Ampere per Square Meter) - Anode Current Density is a measure of the flow of electric charge through a given area of a conductor from Anode.
Anode Voltage - (Measured in Volt) - Anode Voltage is the anode potential.
Anode Temperature - (Measured in Kelvin) - Anode Temperature is a physical quantity that describes the level of thermal energy in a system, or the degree of hotness or coldness of Anode.
STEP 1: Convert Input(s) to Base Unit
Cathode Current Density: 0.47 Ampere per Square Centimeter --> 4700 Ampere per Square Meter (Check conversion here)
Cathode Voltage: 1.25 Volt --> 1.25 Volt No Conversion Required
Cathode Temperature: 1350 Kelvin --> 1350 Kelvin No Conversion Required
Anode Current Density: 0.26 Ampere per Square Centimeter --> 2600 Ampere per Square Meter (Check conversion here)
Anode Voltage: 0.98 Volt --> 0.98 Volt No Conversion Required
Anode Temperature: 1050 Kelvin --> 1050 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Qc = Jc*(Vc+(2*[BoltZ]*Tc)/[Charge-e])-Ja*(Va+(2*[BoltZ]*Ta)/[Charge-e]) --> 4700*(1.25+(2*[BoltZ]*1350)/[Charge-e])-2600*(0.98+(2*[BoltZ]*1050)/[Charge-e])
Evaluating ... ...
Qc = 3950.0329836919
STEP 3: Convert Result to Output's Unit
3950.0329836919 Watt per Square Meter -->0.39500329836919 Watt per Square Centimeter (Check conversion here)
FINAL ANSWER
0.39500329836919 ≈ 0.395003 Watt per Square Centimeter <-- Cathode Net Energy
(Calculation completed in 00.008 seconds)
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Created by Nisarg
Indian Institute of Technology,Roorlee (IITR), Roorkee
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Verified by Parminder Singh
Chandigarh University (CU), Punjab
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9 Thermal Power Plant Calculators

Net Rate of Energy Supply to Cathode
Go Cathode Net Energy = Cathode Current Density*(Cathode Voltage+(2*[BoltZ]*Cathode Temperature)/[Charge-e])-Anode Current Density*(Anode Voltage+(2*[BoltZ]*Anode Temperature)/[Charge-e])
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)
Output Voltage given Anode and Cathode Work Functions
Go Output Voltage = Cathode Work Function-Anode Work Function
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

Net Rate of Energy Supply to Cathode Formula

Cathode Net Energy = Cathode Current Density*(Cathode Voltage+(2*[BoltZ]*Cathode Temperature)/[Charge-e])-Anode Current Density*(Anode Voltage+(2*[BoltZ]*Anode Temperature)/[Charge-e])
Qc = Jc*(Vc+(2*[BoltZ]*Tc)/[Charge-e])-Ja*(Va+(2*[BoltZ]*Ta)/[Charge-e])

What are the advantages of Thermionic Power Generators?

There are certain advantages to thermionic generators over other energy converters, such as a traditional Carnot heat engine, which converts heat into mechanical energy in the form of work. One benefit of the thermionic process is that there are no moving pars in the system, which allows for very long operational lifetimes. Furthermore, thermionic converters can be fabricated at a much smaller scale than the Carnot engine, which opens the door for possibilities of thermal energy conversion at the microscale.

How to Calculate Net Rate of Energy Supply to Cathode?

Net Rate of Energy Supply to Cathode calculator uses Cathode Net Energy = Cathode Current Density*(Cathode Voltage+(2*[BoltZ]*Cathode Temperature)/[Charge-e])-Anode Current Density*(Anode Voltage+(2*[BoltZ]*Anode Temperature)/[Charge-e]) to calculate the Cathode Net Energy, The Net Rate of Energy Supply to Cathode formula is defined as the total energy supplied to the cathode. Cathode Net Energy is denoted by Qc symbol.

How to calculate Net Rate of Energy Supply to Cathode using this online calculator? To use this online calculator for Net Rate of Energy Supply to Cathode, enter Cathode Current Density (Jc), Cathode Voltage (Vc), Cathode Temperature (Tc), Anode Current Density (Ja), Anode Voltage (Va) & Anode Temperature (Ta) and hit the calculate button. Here is how the Net Rate of Energy Supply to Cathode calculation can be explained with given input values -> 0.395003 = 4700*(1.25+(2*[BoltZ]*1350)/[Charge-e])-2600*(0.98+(2*[BoltZ]*1050)/[Charge-e]).

FAQ

What is Net Rate of Energy Supply to Cathode?
The Net Rate of Energy Supply to Cathode formula is defined as the total energy supplied to the cathode and is represented as Qc = Jc*(Vc+(2*[BoltZ]*Tc)/[Charge-e])-Ja*(Va+(2*[BoltZ]*Ta)/[Charge-e]) or Cathode Net Energy = Cathode Current Density*(Cathode Voltage+(2*[BoltZ]*Cathode Temperature)/[Charge-e])-Anode Current Density*(Anode Voltage+(2*[BoltZ]*Anode Temperature)/[Charge-e]). Cathode Current Density is a measure of the flow of electric charge through a given area of a conductor from Cathode, Cathode Voltage is the cathode potential, Cathode Temperature is a physical quantity that describes the level of thermal energy in a system, or the degree of hotness or coldness of Cathode, Anode Current Density is a measure of the flow of electric charge through a given area of a conductor from Anode, Anode Voltage is the anode potential & Anode Temperature is a physical quantity that describes the level of thermal energy in a system, or the degree of hotness or coldness of Anode.
How to calculate Net Rate of Energy Supply to Cathode?
The Net Rate of Energy Supply to Cathode formula is defined as the total energy supplied to the cathode is calculated using Cathode Net Energy = Cathode Current Density*(Cathode Voltage+(2*[BoltZ]*Cathode Temperature)/[Charge-e])-Anode Current Density*(Anode Voltage+(2*[BoltZ]*Anode Temperature)/[Charge-e]). To calculate Net Rate of Energy Supply to Cathode, you need Cathode Current Density (Jc), Cathode Voltage (Vc), Cathode Temperature (Tc), Anode Current Density (Ja), Anode Voltage (Va) & Anode Temperature (Ta). With our tool, you need to enter the respective value for Cathode Current Density, Cathode Voltage, Cathode Temperature, Anode Current Density, Anode Voltage & Anode Temperature 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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