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.

It is reasonable to assume that the bulk modulus of blood is about the same as that of water (2.2 gpa). as one goes deeper and deeper in the ocean, the pressure increases by 10000 pa for every meter below the surface. if a diver goes down 80.0 m in the ocean, by how much does each cubic centimeter of her blood change in volume? give the answer in cubic centimeters (actually one cubic centimeter equals one milliliter).

How do you know how many valence electrons an atom has?

The inside surface of a cylindrical-shaped cave of inner diameter 1.0 m is continuously covered with a very thin layer of water. the cave is very long and it is open on both ends. the water on the cave surface is at a constant temperature of 15.5 °c. the cave is constantly exposed to wind such that 15.5 °c air flows through the cave at 4.5 m/s. the kinematic viscosity of the air is 14.66 x 10-6 m2/s and the molecular diffusion coefficient of water vapor in the air is 0.239 x 10-4 m2/s. because the cave diameter is so large, the flow of wind down the length of the cave, in the x direction, can be treated like it is external flow and the cave surface can be approximated as flat where appropriate. calculate the x value, in a) the transition to turbulent flow occurs at rex meters, where the air flow transitions from laminar to turbulent along the inside surface of the cave b) calculate the x value, in meters, where the bulk steady state concentration of water vapor in the air flowing in the cave is 10% of the saturation concentration. assume the air at the surface of the water layer is 100% saturated with water vapor. assume the wind entering the cave contained no moisture before it entered the cave. take into account the transition from laminar to turbulent flow when solving part b