Percent change in thermionic emission

[benben312000]

% change in thermionic emission

Q1. Determine the % change in thermionic emission for an oxide-coated filament of work function of 1.3eV if the temperature is decreased by 1.00% at a temperature of 2300K

I'm uncertain but i used

dJ/J=dT/T ( 2 + ((1160x1.3)/1000)

to get a 15% change in current density. I'm not really good at this so i not sure if i used the formula correctly

Q2. Calculate the % change in therimonic amission from tungsten filament of work function 4.52eV if the work funtion is decreased by 1.00% at a temperature of 2300K

I was really puzzled by this question as the difference is in this question the work function is said to decrease but i do not know how to calculate the % change.

Thanks in advance for all the help given.

 

[rude man]

Use the old (1901, Richardson) formula for thermionic emission:
J = K(T^2)exp(-W/kT),

J = thermionic current density
K = constant peculiar to emitting oxide,
W = work function of oxide
T = temperature, Kelvin.

 

[benben312000]

Thanks lots Rude man

Hmm that's interesting i came across a Richardson-Dushmann law as well but it's not so similiar, but that's how i get the "dJ/J=dT/T ( 2 + ((1160x1.3)/1000)". But it's differentiate with respect to the absolute temperature.

Btw do u mean i could use the same formula for both the question cause i don't understand the 2nd question.

Thanks once again

 

[rude man]

Thanks lots Rude man

Hmm that's interesting i came across a Richardson-Dushmann law as well but it's not so similiar, but that's how i get the "dJ/J=dT/T ( 2 + ((1160x1.3)/1000)". But it's differentiate with respect to the absolute temperature.

Btw do u mean i could use the same formula for both the question cause i don't understand the 2nd question.

Thanks once again

Yes, the formula isused for both of your questions. Just need a bit of calculus:

dJ/J = (1/J)∂J/∂T*dT + (1/J)∂J/∂W*dW

For your 1st problem, W is constant.
For your 2nd problem, T is constant.
Away you go!

PS - from Wikipedia: "Over 60 years later, there is still no consensus amongst interested theoreticians as to what the precise form of the expression for K should be ... "

PPS - for you that makes no difference since K will cancel out when you divide by J.

 

[DeeNos]

I would like to clarify a few things before providing a response. First, it is important to note that thermionic emission refers to the process of electrons being emitted from a heated surface. The term "percent change in thermionic emission" is not a commonly used scientific term. It is important to have a clear understanding of the specific scenario and parameters being discussed in order to accurately calculate any changes.

In Q1, the scenario is discussing a change in temperature for an oxide-coated filament with a work function of 1.3eV. It is unclear what the starting temperature is, but assuming it is also 2300K, the formula you have used (dJ/J=dT/T ( 2 + ((1160x1.3)/1000)) would not be applicable in this case. This formula seems to be a combination of the equations for current density (J=AT^2e^(-phi/kT)) and percent change (dX/X = dT/T). However, in this scenario, we are not interested in the current density but rather the thermionic emission, which is dependent on the work function and temperature.

To calculate the percent change in thermionic emission, we would need to know the initial and final values of the work function and temperature. Without this information, we cannot accurately calculate the change.

In Q2, the scenario is discussing a change in work function for a tungsten filament with a work function of 4.52eV. Again, it is unclear what the starting work function is, so we cannot accurately calculate the percent change. However, if we assume the starting work function is also 4.52eV and it decreases by 1.00%, the new work function would be 4.47eV. To calculate the change in thermionic emission, we would need to use the equation J=AT^2e^(-phi/kT) and plug in the new work function value.

In summary, it is important to have clear and specific parameters in order to accurately calculate any changes in thermionic emission. Additionally, using the correct equations and units is crucial in scientific calculations.