= 90 atm, and at a temperature T2 = 350 K the pressure is p, =
= 110 atm. Find the Van der Waals parameters for this gas.
2.24. Find the isothermal compressibility x of a Van der Waals
gas as a function of volume V at temperature T.
Note. By definition, x = — I. ay
2.25. Making use of the result obtained in the foregoing problem,
find at what temperature the isothermal compressibility x of a Van
der Waals gas is greater than that of an ideal gas. Examine the case
when the molar volume is much greater than the parameter b.
2.2. The First Law of Thermodynamics. Heat Capacity
- The first law of thermodynamics:
Q= + A ,
where AU is the increment of the internal energy of the system.
- Work performed by gas:
A= p dV. - Internal energy of an ideal gas:
m RT pV
U C vT =— —
M M y-1 y -1 • - Molar heat capacity in a polytropic process (p Vn = const):
(n— R
C — — 1 n — 1 (n — 1) (17 — 1) ' - Internal energy of one mole of a Van der Waals gas:
U=CvT— V a m (^)
2.26. Demonstrate that the interval energy U of the air in a room
is independent of temperature provided the outside pressure p is
constant. Calculate U, if p is equal to the normal atmospheric pres-
sure and the room's volume is equal to V = 40 m 3.
2.27. A thermally insulated vessel containing a gas whose molar
mass is equal to M and the ratio of specific heats C pICv = y moves
with a velocity v. Find the gas temperature increment resulting from
the sudden stoppage of the vessel.
2.28. Two thermally insulated vessels 1 and 2 are filled with air
and connected by a short tube equipped with a valve. The volumes
of the vessels, the pressures and temperatures of air in them are
known (V 1 , pi, T 1 and V 2 , p 2 , 7' 2 ). Find the air temperature and
pressure established after the opening of the valve.
2.29. Gaseous hydrogen contained initially under standard con-
ditions in a sealed vessel of volume V = 5.0 1 was cooled by AT =
(2.2a)
(2.2b)
(2.2c)
(2.2d)
(2.2e)