Recent content by baseballfan_ny

1.1) I see 4-fold rotational symmetry about the axis going through the center of the diffraction pattern perpendicular to the plane of the page 1.2) and 1.3) This is where I'm stuck. Once I get the horizontal spacing between adjacent lattice points, ##d^*##, the repeat distance in the crystal...

The idea here (as I'm told) is to use the boundary conditions to get a transcendental equation, and then that transcendental equation can be solved numerically. So I'm making a few assumptions in this problem: 1. The potential ##V(x)## is even, so the wavefunction ##\psi(x)## is either even or...

Here is a diagram of my interpretation of the problem: Where I'm thinking that the engine originally takes heat from ##T_h## to ##T_l##, in which case ## \frac { Q_{h} } { T_{h} } = \frac { Q_{l} } { T_{l} } ## and ## W_{out} = Q_{in} - Q_{out} = Q_h \left( 1 - \frac {T_l} {T_h} \right) ##...

So for part a, I separately minimized F wrt ##\theta## and ##P## and got the following. $$\frac {\partial f} {\partial \theta} = a_{\theta}(T-T_{\theta})\theta + b_{\theta}\theta^3 - tP = 0$$ $$ \frac {\partial f} {\partial P} = \alpha(T-T_P)P -t\theta$$ $$ P = t\theta \alpha (T-T_P) $$ Then...

Works! Thank you!

So a and b were pretty straightforward. Got stuck on part c. The question says they approximated Van der Waals in first order in a and b. So I started with that by rewriting Van der Waals eqn as ## p = \frac { N \tau } { V - Nb } - \frac {N^2a} {V^2} ## and I then Taylor approximated ## \frac...

My idea was that the total amount of energy emitted by sheet 1 = total amount of energy "delivered" to sheet 1 (I realized I wrote "absorbed" instead of "delivered" in Post 1 so that was probably confusing). The first term is the energy emitted by sheet 1, since it has absorptivity = emissivity...

But ##T_3## = 0, so it doesn't emit any energy, right? I suppose it can absorb energy emitted by ##P_{23}##. I had thought that originally ... that ##P_{23} = A\sigma_B T_2^4##, but I think there has to be equilibrium maintained? So that's why applied those conditions. I just don't think it...

I need someone to check my work, because I'm getting weird results that I'm not able to interpret physically for parts b and c. Thanks in advance. For part a... ##J_u = e_1 \sigma_B T^4## ##P_1 = AJ_u = e_1 \sigma_B AT_1^4## ## T_1 = \left( \frac {P_1} {e_1 \sigma_B A} \right)^{\frac 1 4} ##...

This is exactly the hint I needed and it worked perfectly. I apologize for the late acknowledgment. Thanks for the help!

Thanks for sharing!

Oh gosh, was it really that simple? lol. Then I get ##N_1 = \frac {N} {2} + \frac {\Delta} {4c}## ##N_2 = \frac {N} {2} - \frac {\Delta} {4c}##. I still must have done something wrong when minimizing free energy in the first part of Post 3, because that gave me ##N_1## = ##N_2##.

I just thought of another idea if anyone else is able to help... maybe when the problem states the system should be in diffusive equilibrium, it means just diffusive equilibrium and not thermal equilibrium so the potential difference could be a part of some sort of thermal imbalance? (actually...

Thanks all for the help! So physics-wise, all this model is saying is that pressure decreases exponentially with altitude and temperature decreases linearly with altitude (assuming ##\gamma## > 1, which I suppose it would be cause I think it gets colder as you go higher). I don't really know...

Makes sense. But I'm still getting ##\Delta = 0## and I think I'm a bit confused on the distinctions between internal and external chemical potential. So for minimizing the free energy, I'm doing this: $$ dF = \left( \frac {\partial F_1} {\partial N_1} \right)_{T,V} dN_1 + \left( \frac...