One Hour The Pressure Inside The Container example essay topic

Thermal Physics - 340 Exam #1 Due Monday, February 18th, at the start of class As discussed in class, submission of your solutions to this exam will indicate that you have not communicated with others concerning this exam. You may use reference texts and other information at your disposal. Do all problems separately on clean white standard 8.5" X 11" photocopier paper (no notebook paper or scratch paper). Write on only one side of the paper (I don't do double sided). Staple the entire solution set in the upper left hand corner (no binders or clips). Don't turn in pages where you have scratched out or erased excessively, re-write the pages cleanly and neatly.

All problems are equally weighted. Assume we are working with "normal" pressures and temperatures with ideal gases unless noted otherwise. Make sure you list all assumptions that you use (symmetry, isotropy, binomial expansion, etc. ). 1. A container has one wall which contains many small holes, and outside the container is vacuum.

If the container is filled with He at pressure Po, it is found that after one hour the pressure inside the container is Po/2. The container is now filled with an equal number of He and Ne atoms to a total pressure of Po. (a). Calculate the ratio of the number of Ne to He atoms left in the container after one hour. (b). Would this problem be more difficult if the atoms were initially C and H?

Explain from two standpoints, the realistic standpoint and the physics-land standpoint. The latter explanation should invoke the assumptions made in the ideal gas model, the former something you know about chemistry. (c). Explain why such a container might be useful in the case of isotopes, especially a series of such containers set up so that what comes out of the first goes into the second and so on. 2. A He and H atom collide elastically in a head-on collision. (a). If they have the same kinetic energy (KE) to begin with, which one gains KE?

Answer this by calculating the amount gained and lost for both, relative to their initial value. (b). Suppose the atoms had the same mass but different kinetic energies? Do not do a detailed calculation here, but instead make a physical argument as to why the "slower" thus "cooler" atoms would slow down the faster, hotter atoms. This is one process for the moderation of hot neutrons in a nuclear fission reactor by the water used as its coolant. 3. A person has some hot coffee of mass M at temperature Th and some room temperature "creamer" of mass m.

Assume the specific heats of both liquids is one, that M m, and neglect their containers. The person wants to drink the coffee + creamer mixture after waiting a certain time t, and wants the mixture to be as cool as possible. Should the person (a) dump in the creamer and then wait for time t, or (b) wait for time t and then dump in the creamer? Answer this by calculating the temperature of the mixture under both scenarios (a and b), and showing that one is larger than the other. Assume the rate of thermal energy loss by the hotter object to the colder surroundings is linearly proportional to the temperature difference between the two, where the constant of proportionality (call it α ) is independent of the mass of the object. For simplicity, choose a temperature scale linear with the Kelvin scale (like Celsius), but offset such that room temperature is the best number in physics (zero).

This exponential-type of cooling is sometimes referred to as "Newton's Law of Cooling". (c) Why is the assumption that α is independent of mass not a good one in the case of an open cup of coffee? 4. Consider the simple harmonic oscillator problem with three independent degrees of freedom (DOF) (i.e. one particle in a 3-D box or 3 particles in a 1-D box), where the energy of each DOF is given by (n + 1/2) ω where n is the quantum number for that DOF. (a). Assume ω = ω o, and make a table of all the micro states that give rise to the macro states we would call the ground state up through the third excited state. List the total energy and multiplicity of each macro state. (b). Now assume ω = 2ω o, and make the same table. (c).

Compare the entropy of the two systems for all the macro states with energies E ≤ 5 ω o. Generalize your findings to a statement about how the entropy of a system depends on the energy level spacings, and extend this to the case of a "continuous" energy distribution and the density of states. Comment on whether you think your generalization would differ if the systems in (a) and (b) had the same ground state energies. 5. (a). Draw a T-S plot for a standard "slow" Carnot engine cycle. Explain what the area inside the curve means physically, and how to determine the efficiency of the engine right from the graph. Draw two more such plots using the same Th, one for a Carnot engine with low efficiency and one with a high efficiency. (b).

Does the shape or size of these diagrams depend on the working fluid of the engine? Explain. (c). Explain why T-S diagrams can only be used for reversible processes. 6. Consider an adiabatic enclosure of total volume V with a partition down the middle.

Each side contains the same number of moles of an ideal gas, but they are different gases. The partition is removed quickly without disturbing the system so it is neglected. Assume that the diffusive mixing of the gases that follows is equivalent to two separate free expansions, one for each gas. (a). Determine the entropy change of the universe for this irreversible mixing process. (b). What would happen to your answer if you had not neglected the removal of the partition, but instead had to consider how and by what it was removed? (c). The second law is sometimes stated as S (universe) ≥ 0 for all processes, the equality only holding for reversible processes.

Are there any assumptions built into this statement? Explain.