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

If this plastic cup is heated to its melting point, what will eventually happen to all the particles in the plastic? a. the particles will begin to move enough that they slide past each other. b. bonds will form and the liquid will become a solid. c. the spaces between the particles will get smaller. d. the particles will change state and become a crystalline solid.

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.

Ablock of mass m slides on a horizontal frictionless table with an initial speed v0 . it then compresses a spring of force constant k and is brought to rest. the acceleration of gravity is 9.8 m/s2. how much is the spring compressed x from its natural length? 1) x = v0*sqrt(k/(mg)) 2) x=v0*sqrt(m/k) 3) x=v0*((mk)/g) 4) x=v0*sqrt(k/m) 5) x=v0*(m/kg) 6) x=v0*sqrt((mg)/k) 7) x=(v0)^2/(2g) 8) x=v0*(k/(mg)) 9) x=(v0)^2/(2m) 10) x=v0*((mg)/k)