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Percent change in thermionic emission

  1. Dec 31, 2011 #1
    % 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.
     
  2. jcsd
  3. Jan 3, 2012 #2

    rude man

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    Re: % change in thermionic emission

    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.
     
  4. Jan 5, 2012 #3
    Re: % change in thermionic emission

    Thanks lots Rude man o:)

    Hmm thats interesting i came across a Richardson-Dushmann law as well but it's not so similiar, but thats 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 dont understand the 2nd question.

    Thanks once again
     
  5. Jan 5, 2012 #4

    rude man

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    Re: % change in thermionic emission

    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.
     
    Last edited: Jan 5, 2012
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