Thermodynamics, Statistical Physics, and Quantum Mechanics

90

During the sublimation of the ice,the acceleration of the astronaut is

where corresponds to themomentumtransferred by themolecules
leaving thesurface. Using thetime calculatedabove, he willcover a
distance

Note that this is thelowerlimit because weassumed andthat all the
moleculesthat areleaving go toinfinity. So, itseems that theastronaut
can cover the distance to the ship by using his cup as anengine. Moreover,
the sticking coefficient which is oftenassumed to beclose tounity,could
be much smaller (for water, at 0°C). That explains why the
water in a cup left in aroomdoes notevaporate in amatter ofminutes
but rather in a few hours. For a detailed discussion see E. Mortensen
and H. Eyring, J.Phys. Chem. 64, 846 (1960). The physical reason for
such a smallsticking coefficient in water isbased on thefactthat in the
liquidphase therotationaldegrees offreedom arehindered, leading to a
smallerrotational partitionfunction. So, themoleculeswhose rotation
cannotpass adiabaticallyinto theliquid will berejected and reflectback
into the gaseous phase. These effects are especiallystrong in asymmetric
polarmolecules (such aswater). Theactualtime the teacupengine will
be working is significantly longer(about 30times, if weassumethat the
sticking coefficient for ice is about thesame as forwater at

4.7 Grand Lunar Canals (Moscow Phys-Tech)

Consider theatmosphere to be isothermal inside the channel. Thepres-
sure depends only on the distance from thecenter of themoon (see
Figure S.4.7), andas in Problem4.19 we have

So

SOLUTIONS