# Homework Help: Percent change in thermionic emission

1. Dec 31, 2011

### 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.

2. Jan 3, 2012

### rude man

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.

3. Jan 5, 2012

### benben312000

Re: % change in thermionic emission

Thanks lots Rude man

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

4. Jan 5, 2012

### rude man

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