m2( MI- Heat and Molecular Physics
2.1. Since the vertical cylinders are communicating
vessels, the equilibrium sets in after the increase
in the mass of the first piston only when it "sinks"
to the bottom of its cylinder, i.e. the whole of the
gas flows to the second cylinder. Since the tem-
perature and pressure of the gas remain unchanged.
the total volume occupied by the gas must remain
unchanged. Hence we conclude that Siho S 2 h o =
S 2 h, where Si and S2 are the cross-sectional areas
of the first and second cylinders, and h is the height
at which the second piston will be located, i.e.
just the required difference in heights (since the
first piston lies at the bottom). The initial pressures
produced by the pistons are equal. Therefore,
m2g
Si S 2
Si ml
S2 m 2and hence+1 ) = 0.3 m.2.2. If the temperature Twaii of the vessel walls
coincides with the gas temperature T, a molecule
striking the wall changes the normal component
p, of its momentum by —px. Consequently, the
total change in the momentum is 2px. When
Twaii > T, the gas is heated. This means that gas
molecules bounce off the wall at a higher velocity
than that at which they impinge on the wall,