Exam II Results Avg. 33.8=56%. Exam questions 1.A typical neutron star has a radius of 12 km and a density of roughly 5x10 17 kg/m 3 (which is only slightly.

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tsExam II ResultsAvg. 33.8=56%

Exam questions1. A typical neutron star has a radius of 12 km and a density of roughly 5x1017 kg/m3 (which is only slightly greater

than the density of large nuclei). Although the structure of such stars can be quite complicated, for the purposes of this question, let’s assume that it consists simply of a gas of non-interacting non-relativistic neutrons at a temperature of 106 K.

a. (10 points) Determine the Fermi temperature of the neutron star. Would you expect the assumption that the neutrons are non-relativistic to be a good one?

b. (5 points) Estimate the heat capacity at constant volume for this star within the model described.

2. Consider a small sphere of silver (r=1.5 cm) painted with a thin layer of material that permits it to act as a perfect black body. The sphere consists of roughly 2.5x1025 silver atoms, and silver has a Debye temperature of 225 K. The sphere is released into deep interstellar space (say somewhere out beyond Pluto) at an initial temperature of 400K.

a. (10 points) Estimate the initial rate at which the temperature of the sphere will drop (you may assume that the heat transfer is dominated by radiation, and that the heat capacity is dominated by atomic vibrations of the silver atoms).

b. (10 points) What would you expect to be the final temperature of the sphere, and what would you expect to be the heat capacity (at constant volume) due to its atomic vibrations to be at this temperature?

Phase Transitions

http://en.wikipedia.org/wiki/Phase_transition

The above picture shows a block of solid Ar melting and subliming after exposur to aire at roughly room temperature.

Phase Diagram of H2O

http://people.virginia.edu/~lz2n/mse209/Chapter9-p1.pdf

See also: http://www1.lsbu.ac.uk/water/phase.html

Examples Chapter 124.) A system consists of 1024 molecules of water. The initial state is pure

vapor at 373 K and atmospheric pressure. The water is heated at constant pressure to T=700K, subsequently compressed isothermally to a pressure of 230 atm, cooled to 373 K a this constant pressure, and finally allowed to expand isothermally to atmospheric pressure. The final state is pure liquid.a) What is the net change in the system’s internal energy?b) What is the net change in the system’s chemical potential?

5). The top of Mt. Everest is 8,854 meters above sea level. Calculate the temperature at which water boils at the summit.

7). The vapor-pressure curves at the triple point display a cusp (if you look carefully enough, and if the person drawing the diagram was careful enough). Explain why this must be the case.

a). Specifically, near the triple point for water vg/vl=2.06x105 vs/vl=1.09 and the latent heats are 0.47, 0.53 and 0.062 eV/molecule (for vaporization, sublimation and melting respectively).

Phase Diagram of H2O

http://people.virginia.edu/~lz2n/mse209/Chapter9-p1.pdf

See also: http://www1.lsbu.ac.uk/water/phase.html

3He

From J.R. Waldram“The Theory of Thermodynamics”

Alloy phase diagram of Cu-Ni

http://people.virginia.edu/~lz2n/mse209/Chapter9-p1.pdf

Eutectic Phase Diagram

http://www.tulane.edu/~sanelson/geol212/2compphasdiag.html

NOTE: at a given overall composition (say: X), both the relative amounts of the two phases (a,b or c,d) AND the composition of one (or possibly both) depend on the temperature

Van der Waals Isotherms

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Maxwell construction