Proving Maclaurin Series for 1st Law of Blackbody Radiation

Join the discussion
Registration is free. Start your own thread to ask a follow-up.
2 replies · 2K views
Pietervv
Messages
6
Reaction score
0
My homework question is about the first law of blackbody radiation. I have to prove an expansion when
for KT≫ℏw.
After some rewriting of the formula i have (ex-1)-1

because KT≫ℏw, x is close to zero, so i think i should use the maclaurin series.

According Wolfram Alpha the series expansion is [PLAIN]http://www5b.wolframalpha.com/Calculate/MSP/MSP32441h2h6354114hd8ba00002hih32dh1h5ch337?MSPStoreType=image/gif&s=14&w=174.&h=59. and this is exactly what i have to prove. But i have no idea how to come here. I tried to use all my knowledge but i don't even come close to the expansion that it should be...

So my question is: what are the steps from (ex-1)-1 to [PLAIN]http://www5b.wolframalpha.com/Calculate/MSP/MSP32441h2h6354114hd8ba00002hih32dh1h5ch337?MSPStoreType=image/gif&s=14&w=174.&h=59.
 
Last edited by a moderator:
Physics news on Phys.org
Pietervv said:
My homework question is about the first law of blackbody radiation. I have to prove an expansion when
for KT≫ℏw.
After some rewriting of the formula i have (ex-1)-1


because KT≫ℏw, x is close to zero, so i think i should use the maclaurin series.

According Wolfram Alpha the series expansion is [PLAIN]http://www5b.wolframalpha.com/Calculate/MSP/MSP32441h2h6354114hd8ba00002hih32dh1h5ch337?MSPStoreType=image/gif&s=14&w=174.&h=59. and this is exactly what i have to prove. But i have no idea how to come here. I tried to use all my knowledge but i don't even come close to the expansion that it should be...

So my question is: what are the steps from (ex-1)-1 to [PLAIN]http://www5b.wolframalpha.com/Calculate/MSP/MSP32441h2h6354114hd8ba00002hih32dh1h5ch337?MSPStoreType=image/gif&s=14&w=174.&h=59.


First, find the expansion for ##e^x - 1##. Then think Binomial.
 
Last edited by a moderator:
Pietervv said:
My homework question is about the first law of blackbody radiation. I have to prove an expansion when
for KT≫ℏw.
After some rewriting of the formula i have (ex-1)-1


because KT≫ℏw, x is close to zero, so i think i should use the maclaurin series.

According Wolfram Alpha the series expansion is [PLAIN]http://www5b.wolframalpha.com/Calculate/MSP/MSP32441h2h6354114hd8ba00002hih32dh1h5ch337?MSPStoreType=image/gif&s=14&w=174.&h=59. and this is exactly what i have to prove. But i have no idea how to come here. I tried to use all my knowledge but i don't even come close to the expansion that it should be...

So my question is: what are the steps from (ex-1)-1 to [PLAIN]http://www5b.wolframalpha.com/Calculate/MSP/MSP32441h2h6354114hd8ba00002hih32dh1h5ch337?MSPStoreType=image/gif&s=14&w=174.&h=59.
What do KT and ℏw have to do with (ex - 1)-1?

Per Physics Forums rules, homework questions need to be posted using the homework template, which includes a complete problem statement. I am locking this thread. Please start a new thread with the information that's needed.
 
Last edited by a moderator: