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## Homework Statement

Part(a): explain the meaning of f(v) and A.

Part(b): Gas from surrounding air effuse into a box; find the temperature in the box.

Part (c): Explain why initial temperature of gas escaping from first box into second is the same as temperature in first box.

Part (d): Find equilibrium temperature of second box after a long time.

## Homework Equations

## The Attempt at a Solution

**Part(b)**[tex]Flux = \frac{1}{4}n<v> = \frac{1}{4} \frac {P_{air}}{kT_{air}} <v_{air}> [/tex]

I assume RHS is constant, so flux entering the chamber is constant as the surrounding air is much more massive than the box.

[tex]\frac{PV}{kT} = \frac{1}{4} \frac {P_{air}}{kT_{air}} <v_{air}> [/tex]

If the box is thermally isolated, I can't assume temperature of box = temperature of air. Also, I do not know the pressure in the box. Without the pressure, I can't solve for temperature.

**Part(c)**I suppose temperature is the measure of average KE of molecules, so the first few molecules escaping into the second box should have the same temperature as molecules in the first box. After some time, the temperature changes because pressure inside second box changes?

**Part(d)**After a long time, equilibrium has been established.

Flux out of second box = flux into second box

[tex] \frac{1}{4}n_2<v_2> = \frac{1}{4}n_1<v_1> [/tex]

[tex] \frac {P_2}{T_2} (\sqrt{T_2}) = \frac {P_1}{T_1} (\sqrt{T_1}) [/tex]

[tex]\frac {P_2}{\sqrt{T_2}} = \frac {P_1}{\sqrt{T_1}} [/tex]

I'm not sure what the pressures are...