Show that the pressure exerted by a Fermi gas at absolute zero is

p = (2NEf)/(5V)

where N is the total number of particles, Ef the fermi energy and V is the volume.

((If you need to use the relation for the mean energy <E> of particles obeying Fermi-Dirac statistics at absolute zero temperature, you can just quote it's <E> = 3Ef/5 I derived it earlier in this problem, so you don't have to derive it again))

Solution Summary

In free electron theory , the electrons are considered as particles with half integral spins and so Fermions. The present problem describes the derivation of the pressure exerted by fermi gas at absolute zero.

Given 1 angstrom unit = 10 ^-10 m and 1 fermi = 10 ^--15 m , what is the
a. 1 angstrom = 10^5 fermi
b. 1 angstrom = 10^-5 fermi
c. 1 angstrom = 10^-25 fermi
d. 1 angstrom = 10^25 fermi
e. 1 angstrom = 10^-15 fermi

Four tanks of gas, labeled A, B, C, and D are stored under different conditions. The gases in these tanks are then placed into a fifth, tank E. Eventually, the combined gases reach a temperature which is that of the 25 degrees celcius room. What will be the gauge pressure of the final sample? Tank information for each tank is

Sketch, using either Matlab or Excel on the same axes, the energy/probability distribution curve for n-type silicon at two temperatures T1 and T2 (where T2 > T1) to show the effect of temperature upon the position of the Fermi level. (Hint: where would the Fermi level be if all the silicon atoms contributed a hole-electron pair?

Q: If 1500lb of air is pumped into a previously empty 900ft^3 storage tank and the air temperature in the tank is uniformly 70 F, what is the air pressure in the tank in atmospheres?
Is it possible to solve this with the perfect gas law (PV = nRT)? Also, please brief description of the difference between the Ideal Gas Law and

A sample of ammonia gas with a volume of 7.0 mL at a pressure of 1.68 atm is compressed to a final volume of 2.7 mL at constant temperature. Use the ideal gas law to calculate the final pressure.
a. 100 atm
b. 2.2 atm
c. 1 atm
d. 4.4 atm

Please do not place your response in a .pdf or .cdx format, but Word documents are okay. Thanks!
Here's the actual problem:
A cylinder with initial volume V contains a sample of gas at pressure p. The gas is heated in such a way that its pressure is directly proportional to its volume. After the gas reaches the volume 3V a

A.) At the start of a trip, a driver adjusts the absolutepressure in her tires to be 2.79 105 Pa when the outdoor temperature is 284 K. At the end of the trip she measures the pressure to be 3.02 105 Pa. Ignoring the expansion of the tires, find the air temperature inside the tires at the end of the trip.
B.) Oxygen for h

A monatomic ideal gas(y=1.67) is contained within a box whose volume is 2.5 m^3. The pressure of the gas is 3.5 x 10^5 Pa. The total mass of the gas is 2.3 kg.
What is the speed of sound in the gas?