THERMODYNAMICS AND STATISTICAL PHYSICS 5rope of extreme tensile strength. The Earth would be propelled through
space to the nearest star via the Archimedes’ force on the balloon, trans-
mitted through the rope to the large staple embedded in suitable bedrock
(seeFigure P.4.3). Estimate theforce on the rope(assuming amassless
balloon). Discuss the feasibility of the Baron’s idea (without using any
generalstatements).4.4 Railway Tanker (Moscow Phys-Tech)
A long, cylindrical tank is placed on a carriage that can slide without
friction on rails (see FigureP.4.4). The mass of the empty tanker is
Initially, the tank is filled with an ideal gas of mass kg
at a pressure atm at an ambient temperature Then
one end of the tank is heated to 335K while the other end is kept fixed at
300 K. Find the pressure in the tank and the new position of the center of
mass of the tanker when the system reaches equilibrium.4.5 Magic Carpet (Moscow Phys-Tech)
Once sitting in heavy traffic, Baron von Münchausen thought of a new kind
of “magic carpet” type aircraft (see FigureP.4.5). The upper surface of the
large flat panel is held at a constant temperature and the lower surface
at a temperature He reasoned that, during collision with the
hot surface, air molecules acquire additional momentum and therefore will
transfer an equalmomentum to the panel. The back of the handkerchief
estimates he was able to make quickly for of such a panelshowed that
if and = 373 K (air temperature 293 K) this panel would be
able to levitateitself and a payload (theBaron) ofabout kg. How did
he arrive at this? Is it reallypossible?