[low temperature ideal boson internal energy in d-space] consider a non-interacting boson system in d-space (o is the old german d and ffrak d) gives this font). (1) show that for d > 2 there is an einstein condensation. (2) its internal energy e is proportional to some power of t, if o > 2 for sufficiently low t. determine the exponent statistical-mechanically. (3) show the same result using thermodynamics. to this end, you may use the following fact: the pv-e relation is independent of statistics,2 although i do not forbid you to do full quantum computation as we did in 3-space.

Visualize the problem and identify special cases first examine the problem by drawing a picture and visualizing the motion. apply newton's 2nd law, ∑f⃗ =ma⃗ , to each body in your mind. don't worry about which quantities are given. think about the forces on each body: how are these consistent with the direction of the acceleration for that body? can you think of any special cases that you can solve quickly now and use to test your understanding later? one special case in this problem is if m2=0, in which case block 1 would simply fall freely under the acceleration of gravity: a⃗ 1=−gj^.

Earth's atmosphere is composed of mostly two gases. name the two gases that make up the majority of the atmosphere and use the pie chart to tell the percentages of each.

Researchers conducted an experiment to identify the effects of three different hand sanitizers on the growth of bacteria. the researchers grew one type of bacteria in twenty-four identical covered petri dishes. then, they opened eighteen petri dishes and applied the three hand sanitizers to six petri dishes each. they left the remaining six petri dishes closed as a control group. when the researchers measured the growth of bacteria two days later, the six dishes that had no hand sanitizer showed the least amount of bacterial growth. the researchers concluded that not using any hand sanitizer would lead to the least bacterial growth. which statement best explains why the researchers’ conclusion was not justified? the experiment tested too many variables. the control group was not treated the same as the experimental group. the sample size of twenty-four petri dishes is not large enough. the single type of bacteria is not adequate to make any conclusions.