(b) the amount of the absorbed heat.
The gas is assumed to be a Van der Waals gas.
2.59. For a Van der Waals gas find:
(a) the equation of the adiabatic curve in the variables T, V;
(b) the difference of the molar heat capacities CI, — Cv as a func-
tion of T and V.
2.60. Two thermally insulated vessels are interconnected by a
tube equipped with a valve. One vessel of volume V 1 = 10 1 contains
v = 2.5 moles of carbon dioxide. The other vessel of volume V 2 =
100 1 is evacuated. The valve having been opened, the gas adiabatic-
ally expanded. Assuming the gas to obey the Van der Waals equation,
find its temperature change accompanying the expansion.
2.61. What amount of heat has to be transferred to v = 3.0 moles
of carbon dioxide to keep its temperature constant while it ex-
pands into vacuum from the volume V 1 = 5.0 1 to V 2 = 10 1? The
gas is assumed to be a Van der Waals gas.
2.3. KINETIC THEORY OF GASES.
BOLTZMANN' S LAW AND MAXWELL'S DISTRIBUTION
- Number of collisions exercised by gas molecules on a unit area of the
wall surface per unit time:
v=^1
4— n (v),where n is the concentration of molecules, and (v) is their mean velocity.
- Equation of an ideal gas state:
p = nkT. - Mean energy of molecules:
(e) =
2— kT,^ (2.3c)where i is the sum of translational, rotational, and the double number of vibra-
tional degrees of freedom.
- Maxwellian distribution:
m (^1) 1/2 -mv2/21a
dN (vx)=- N ( - 2nkT ) e s dvx, (2.3d)
dN (v)= N (^) ( e-mv2/2kT 4:tv2 dv. (2.3e)
2 m \ 3/
2nkT )
- Maxwellian distribution in a reduced form:
dN (u)= N^4 e-u2 U 2 du, (2.3f)where u = v/vp, vp is the most probable velocity.
- The most probable, the mean, and the root mean square velocities of
molecules:
(2.3a)(2.3b)Vp n kT (V) = kT^ kTVsq = -. (^) (2.3g)