Ahh okay thank you both. That's very helpful for the future, and I guess my ignorance here is due to the fact that I've never really worked with a function like that before, but upon reviewing the derivation for the identity it does make sense. I feel pretty stupid for asking something so...
Hmm I really never knew you could have any coefficient in front of x/t/whatever and still use the sin2x + cos2x = 1 identity. Oh well thanks a lot for the input
Homework Statement
We just had a test in my calc 3 class, and I'm pretty sure my teacher has the wrong solution to one of the answers. The question is about finding the speed of a particle given a space curve function r(t) = (cos2t)i + (3t - 1)j + (sin2t)k.
Homework Equations
v(t) =...
Ahh I think I see how to get it now. Basically Emp is the maximum of f(E) so you'd go about this problem how you would any graph to find the maximum, by setting the derivative to 0. By setting all of the constants equal to Q, canceling Q and the exponential function on both sides, i made...
f(E) is just a function of E, with the most probable energy being the energy that most of the molecules have in the system, so should I just compute the value to infinity?
Okay that makes sense...I was going off my teacher's example of how to calculate most probable velocity from the Maxwell-Boltzmann distribution. Any hint on what kind of calculation I need to do to get most probable energy? I'm probably going to feel incredibly stupid once I figure it out...
It is supposed to be e^-E/kT, sorry about that. Unfortunately he made it clear that it's not a gamma function...and integration by parts only causes that term to be 1/2(E)^1/2 and just ends up being more complicated. We have discussed transformation of variables and guassian integrals in class...
I figured out what I was doing wrong (in conjection with using 205 m/s). I should've been using 1.39x10^-25 kg for the mass of krypton. After plugging that in i got y(205m/s) = 0.01133 which brings the area to 10 x .01133 = 0.11 m. A much more sensible answer than 0 haha. Thanks a lot everyone...
Yeah it is, so that doesn't make sense. I also tried subbing in 210 and 200 for the equation and subtracting them and I still get 0, unless I'm just typing it in completely wrong or something
Yeah sorry about that. The Maxwell-Boltzmann distribution is 4*pi*(m/2*pi*k*T)3/2*v2*e-mv2/2kT and obviously ∆x=10 m/s, so I plugged in 10 for v and 0.0838 kg/mol for m and end up with 0 which doesn't make sense...=\
Homework Statement
When it comes to evaluating integrals, there are two ways you can do it. First, you know
that the integration of a function is the area under a curve, as shown in the left hand diagram.
However, if you are looking over a narrow range along the x-axis, you can make an...
Homework Statement
If the Maxwell-Boltzmann distribution of energy is f(E)=2*pi*E1/2*(1/pi*k*T)3/2*eE/kT. Can you calculate the most probable energy from this? (The answer is kt/2).
Homework Equations
Some kind of integration (guassian integral) is needed from 0 to infinity I believe...
I think the answer is going to be something like CH4 and H2 are negative because they possesses essentially no dipoles (especially H2, since it has no intermolecular interactions as H+ ions, much less as inert H2) while He would be weakly positive due to possessing some Van der Waals force and...
Calculate "a" values given equation of state for gases
Homework Statement
For my equation of state:
Vm = (RT/P) - (a/T)
what kind of sign for the constant a (positive or
negative) do you think the following gases will have and why:
a. H2 b. He c. CH4 d. CO2
Hint: There is almost no...