Solutions ions (^211)
and hence have a higher momentum. As a result,
the change in the momentum will be larger than
2Px (Fig. 197).
If, however, Twaii < T, the gas is cooled, i.e.
gas molecules bounce off the wall with a smaller
momentum than that with which they impinge on
the wall. In this case, the change in the momentum
will be obviously smaller than 2p, (Fig. 198).
Twaii=.T
rwcal< T
Fig. 197 Fig. 198
Since according to Newton's second law, the change
in momentum is proportional to the mean force,
the pressure exerted by the gas on the walls is
higher when the walls are warmer than the gas.
2.3. The work A done by the gas during the cycle
is determined by the area of the p-V diagram
bounded by the cycle, i.e. by the area of the trap-
ezoid (see Fig. 57):
( V3-- V2+V4--V1 k
A= (P2,— Pi) 2
) •
All these quantities can easily be expressed in terms
of pressure and volume pi and V 1 at point 1. Indeed,
according to Charles's law, V3 = V 2 T3/ T 2 =
VI T3/ T 2 and V4 VI T 4 / Ti = V 1 7' 2 1T1, while the
Gay-Lussac law implies that p^2 = pi T 217. 1. Sub-
stituting these values into the expression for work,
we obtain
A = Aviv, ( T 2 T 1 1 T2 T3^9
Ti / T^ T^2 I
14*
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