solid consider a three-dimensional simple harmonic os- cillator with mass m and spring constant k (i. e., the mass is attracted to the origin with the same spring constant in all three directions). the hamiltonian is given in the usual way by 2m 2 d calculate the classical partition function note: in this exercise p and x are three-dimensional vectors. d using the partition function, calculate the heat capacity 3kb d conclude that if you can consider a solid to con- sist of n atoms all in harmonic wells, then the heat capacity should be 3nkb 3r, in agreement with the law of dulong and petit. (b) quantum einstein solid now consider the same hamiltonian quantum calculate the quantum partition function where the sum over j is a sum over all eigenstates. d explain the relationship with bose statistics. d find an expression for the heat capacity d show that the high-temperature limit agrees with the law of dulong and petit d sketch the heat capacity as a function of tem- perature (see also exercise 2.7 for more on the same topic)

Which of the following represents an upside-down image?

Need asap ! what is the relationship between atmospheric pressure and the density of gas particles in an area of increasing pressure? (2 points) as air pressure in an area increases, the density of the gas particles in that area decreases. as air pressure in an area increases, the density of the gas particles in that area increases. as air pressure in an area increases, the density of the gas particles in that area remains constant. as air pressure in an area increases, the density of the gas particles in that area increases and decreases in an alternating pattern. 3. which of the following correctly describes a way in which earth's atmosphere interacts with the geosphere? (2 points) it contains gases that living organisms breathe. it contains gases that trap incoming solar radiation. it provides a medium for cycles that provide nutrients to living organisms. it provides a medium for water to move between earth's surface and the air. 4. which of the following is considered a drawback to using wind energy as a source of power? (2 points) wind energy is nonrenewable. wind energy produces large amounts of air pollution. 5. a meteorologist predicts that the weather in a region will soon change from clear skies to probable thunderstorms. prior to making this prediction, what did the meteorologist most likely observe on a barometer? (2 points) the barometer fell slightly. the barometer fell substantially. the barometer rose slightly. the barometer rose substantially. 6. which of the following do meteorologists not typically use weather balloons to record? (2 points) atmospheric pressure cloud types humidity temperature 7. during which step in the can crush lab did water vapor force air from the can? (2 points) the can was filled nearly to the top with water. the can was placed on the hot stove top burner for several minutes. the can was removed from the hot stove top burner. the can was placed upside-down in the water-filled pan.

What is the most useful equation for electric power?