Thermodynamics, Statistical Physics, and Quantum Mechanics

12 PROBLEMS

ure P.4.18). The temperatures and pressures in the two containers are
kept constant and equal to P, and P, respectively. The volume B is
thermallyisolated. Find the equilibrium pressure and temperature in the
ballast volume, assuming the gas is in the Knudsen regime.

Rocket in Drag (Princeton)

A rocket has an effective frontal area A and blasts off with a constant
accelerationa straight up from the surface of the Earth (see Figure P.4.19).

Use either dimensional analysis or an elementary derivation to find out

how the atmospheric drag on the rocket should vary as some power(s)

of the areaA, the rocket velocity and the atmospheric density

(assuming that we are in the region of high Reynoldsnumbers).

Assume that the atmosphere is isothermal with temperature T. De-

rive the variation of the atmospheric density with height Assume

that the gravitational acceleration is a constant and that the density

at sea level is

a)

b)

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