A Vi = 10-3 m3 chamber of a gas bottle contains some argon gas (atomic weight =

Question

A Vi = 10-3 m3 chamber of a gas bottle contains some argon gas (atomic weight = 0.040 kg/mole) at a pressure of 10^4 Pa and a temperature of 25 C.

1)What is the number density of atoms in this chamber? N/V = 2.429909267E24

2)A valve to a new chamber in the bottle is opened, and the gas expands to 3 x 10-3 m3. (The gas does no work in this process because the gas molecules don't have anything moving to push on.) After a while, the parts of the gas re-equilibrate, without exchanging heat with the outside. What is the new temperature, T? T = 25 C

3)In part 2, what is the new pressure, p? p = 3333 Pa

4)The cylinder is now compressed back to the initial volume, slowly enough for it to stay in thermal equilibrium with the walls at the initial temperature 25 C. How much work is needed to do this? W =

Explanation / Answer

1. N/V = 2.429909267E24

2.

There is no work is done since this is free expansion, consider an adiabatic chamber,

there is no heat exchanged with the outside, therefore, the temperature does not change.T = 25oC

3.

new pressure is,

P2 = [V1/V2]P1 = [10-3 / 3 x 10-3]*10^4= 3333 Pa

4.

Number of moles:

n = PV/RT = 10^4*10^-3 / 8.314[25+273] = 0.0040 mol

in this case, the work done:

W = nRTln[V2/V1] = 0.004*8.314*[25+273]*ln[3 x 10-3/10-3] = 10.89 J

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