Consider an 3-dimensional ideal bose gas system whose dispersion relation is given by h2k2 e hw 2m
a) find the mean occupation number of quantum state with a wave vector k.
b) find the total number of particles n_{1} at excited states and internal energy u (t at temperature t and express it in terms of bose-einstein integral gn(z; and thermal wave length h2 1/2 2tmkbt t(

5submission this assignment is worth 20 points total. you are required to submit the following by next lab: 1. (3 points) determine the equation for the output angular velocity ω2 = θ˙ 2 as a function of θ1, ω1 = θ˙ 1 and α. you must show all your work to receive credit. 2. (2 points) use the result of problem#1 to plot ω2 over 0 ≤ θ1 ≤ 360deg with ω1 = 360deg/sec. do this for α = {10,30}deg. show the results on the same plot and properly label the axes, title, legend. for this you can use matlab or ms excel. 3. (3 points) determine the equation for the output angular acceleration ω˙ 2 and create a plot similar to the one in problem#2. 4. (10 points) submit plots of the results (ω2 and ω˙ 2) obtained from creo/mechanism and compare them to results of problem#2 and problem#3. note that you should do these comparisons for the two cases with α = {10,30}deg. 5. (2 points) provide a brief explanation of the results. did they match? what are the implications as misalignment angle increases?

In a heat engine if 1000 j of heat enters the system the piston does 500 j of work, what is the final internal energy of the system if the initial energy was 2000 j? 1. write the equation 2.list out your known variables 3.plug the numbers into the equations 4.solve 5.write your solution statement that includes initial energy and final

Atriangle with equal sides of length 10 cm has -2.5-nc charged objects at each corner. part a determine the direction of the electrical force exerted on the object at the top corner due to the two objects at the horizontal base of the triangle. determine the direction of the electrical force exerted on the object at the top corner due to the two objects at the horizontal base of the triangle. horizontally rightward vertically downward vertically upward horizontally leftward