Consider a classical system of n noninteracting diatomic molecules enclosed in a box of volume v at temperature t. the hamiltonian of the system is taken to be h= where m = 2m the total mass of the molecule, m/2 the reduced mass of the molecule, p is the momentum of the center of mass, pi p2, and p the reduced momentum p = (pi-p2)/2, and r = irl-r21 a calculate the helmholtz free energy, f, of the system. b calculate the internal energy u from the relation u = θ(3f)/a3. does this agree with the result you would get from the equipartition theorem? c what is the specific heat at constant volume? d calculate the mean square molecular diameter < 2 > . you can get this in two ways: from < r2 > = 20(f/n)/ak or from the equipartition theorem. do they agree? e calculate the pressure p =-x/ov.

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

Abucket full of water weights 4 kg and water well is 10m deep. a girl draws water from the well. it takes the girl 3 minutes to draw a bucket full of water from the well. what is the power of the girl?

You have a pick-up truck that weighed 4,000 pounds when it was new. you are modifying it to increase its ground clearance. when you are finished