This are two approaches to this problem, which to take i am not sure. 1. E=h*f>>

Question

This are two approaches to this problem, which to take i am not sure.
1. E=h*f>>>>f=c/lambda so E=(h*c)/lambda,that yields the total energy in the system
then use KE= (DoF) * KT / 2 and solving for T, using 3 degrees of freedom yields 3129K, using 9 degrees of freedom yield 1043K, that is also a dispute, how many degrees of freedom should be used, in my Giancoli textbook i see it using 7 for H2O at most, but the 1043 seems correct since it is very close to the "assumed value" to be used in part B,
2. this approach ignores wavelength and uses the energy of the photon, but this would mean taking the energy of just one photon and not however many photons are in the beam.
KE=(9/2)KT---T=6.63*10^(-20)/(9/2K)=6.63*10^(-20)/(4.5*1.38*10^(-23))=1067.632K also a reasonable number, but still, how many degrees of freedom should be used, within the scope of a physics 2 w/calc class?

Part B is straight forward i believe DeltaQ=M1C1DeltaT+M2C1DeltaT solving for T = 364K

Vrms=Sqrt(3KT/m) = 710 m/s
if we use 9 for DoF or whatever we use should this 3 change to that number also?

please help!!!

Explanation / Answer

It looks like your approaches for #1 and #2 are identical. You seem a little confused by two things: first, E = hc/lamba and E = hf are the same thing. They both express the energy of one photon. You just used f = c/lamda in the first expression. So you used one expression in "solution 1" and the other expression in "solution 2". But they are the same thing. Try it. Calculate E using each.

Next issue: degrees of freedom. A monatomic molecule has 3 deg of freedom. Diatomic molecules have 5. Triatomic molecules have 7. This is why the book uses 7 for water, because it's correct. I'm not sure why you want to use 9, but trying to pick numbers so that your answer matches what you believe should be the right answer is dangerous. Use 7 deg of freedom and calculate the correct answer.

For part b... take a simple weighted average to get the final temperature:

10,000 * your answer from part a + 100,000*300 divided by 110,000

The answer should be much closer to 300 than to your answer from part a.

To find the new v rms, you use vrms = sqrt (3RT/M) where M is molar mass or sqrt(3kt/m) where m is the mass of one molecule. The vrms is only concerned with the the three linear degrees of freedom (i.e. rotation does not affect linear speed), so this expression is the same for all molecules (and that's why the "3" is in the expression.)

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