2.244. Two identical parallel discs have a common axis and are
located at a distance h from each other. The radius of each disc is
equal to a, with a > h. One disc is rotated with a low angular velocity co relative to the other, stationary, disc. Find the moment of
friction forces acting on the stationary disc if the viscosity coefficient of the gas between the discs is equal to
2.245. Solve the foregoing problem, assuming that the discs
are located in an ultra-rarefied gas of molar mass M, at temperature T
and under pressure p.
2.246. Making use of Poiseuille's equation (1.7d), find the mass
of gas flowing per unit time through the pipe of length 1 and radius a
if constant pressures pi and p, are maintained at its ends.
2.247. One end of a rod, enclosed in a thermally insulating sheath,
is kept at a temperature Ti while the other, at T2. The rod is composed of two sections whose lengths are 11 and 12 and heat conductivity coefficients xi and x2. Find the temperature of the interface.
2.248. Two rods whose lengths are li and 12 and heat conductivity
coefficients xi and x2 are placed end to end. Find the heat conductivity
coefficient of a uniform rod of length 11 + /2 whose conductivity
is the same as that of the system of these two rods. The lateral surfaces
of the rods are assumed to be thermally insulated.
2.249. A rod of length 1 with thermally insulated lateral surface
consists of material whose heat conductivity coefficient varies with
temperature as x = air, where a is a constant. The ends of the rod
are kept at temperatures T1 and T2. Find the function T (x), where
x is the distance from the end whose temperature is T1, and
the heat flow density.
2.250. Two chunks of metal with heat capacities C1 and C2 are
interconnected by a rod of length 1 and cross-sectional area S and
fairly low heat conductivity x. The whole system is thermally insulated from the environment. At a moment t = 0 the temperature
difference between the two chunks of metal equals (AT)0. Assuming
the heat capacity of the rod to be negligible, find the temperature
difference between the chunks as a function of time.
2.251. Find the temperature distribution in a substance placed
between two parallel plates kept at temperatures Ti and T2. The
plate separation is equal to 1, the heat conductivity coefficient of
the substance x o -Z-1/ T.
2.252. The space between two large horizontal plates is filled
with helium. The plate separation equals 1 = 50 mm. The lower
plate is kept at a temperature Ti = 290 K, the upper, at T2 =
= 330 K. Find the heat flow density if the gas pressure is close
to standard.
2.253. The space between two large parallel plates separated by
a distance 1 = 5.0 mm is filled with helium under a pressure p =
= 1.0 Pa. One plate is kept at a temperature ti = 17 °C and the
other, at a temperature t 2 = 37 °C. Find the mean free path of helium
atoms and the heat flow density.
located at a distance h from each other. The radius of each disc is
equal to a, with a > h. One disc is rotated with a low angular velocity co relative to the other, stationary, disc. Find the moment of
friction forces acting on the stationary disc if the viscosity coefficient of the gas between the discs is equal to
2.245. Solve the foregoing problem, assuming that the discs
are located in an ultra-rarefied gas of molar mass M, at temperature T
and under pressure p.
2.246. Making use of Poiseuille's equation (1.7d), find the mass
of gas flowing per unit time through the pipe of length 1 and radius a
if constant pressures pi and p, are maintained at its ends.
2.247. One end of a rod, enclosed in a thermally insulating sheath,
is kept at a temperature Ti while the other, at T2. The rod is composed of two sections whose lengths are 11 and 12 and heat conductivity coefficients xi and x2. Find the temperature of the interface.
2.248. Two rods whose lengths are li and 12 and heat conductivity
coefficients xi and x2 are placed end to end. Find the heat conductivity
coefficient of a uniform rod of length 11 + /2 whose conductivity
is the same as that of the system of these two rods. The lateral surfaces
of the rods are assumed to be thermally insulated.
2.249. A rod of length 1 with thermally insulated lateral surface
consists of material whose heat conductivity coefficient varies with
temperature as x = air, where a is a constant. The ends of the rod
are kept at temperatures T1 and T2. Find the function T (x), where
x is the distance from the end whose temperature is T1, and
the heat flow density.
2.250. Two chunks of metal with heat capacities C1 and C2 are
interconnected by a rod of length 1 and cross-sectional area S and
fairly low heat conductivity x. The whole system is thermally insulated from the environment. At a moment t = 0 the temperature
difference between the two chunks of metal equals (AT)0. Assuming
the heat capacity of the rod to be negligible, find the temperature
difference between the chunks as a function of time.
2.251. Find the temperature distribution in a substance placed
between two parallel plates kept at temperatures Ti and T2. The
plate separation is equal to 1, the heat conductivity coefficient of
the substance x o -Z-1/ T.
2.252. The space between two large horizontal plates is filled
with helium. The plate separation equals 1 = 50 mm. The lower
plate is kept at a temperature Ti = 290 K, the upper, at T2 =
= 330 K. Find the heat flow density if the gas pressure is close
to standard.
2.253. The space between two large parallel plates separated by
a distance 1 = 5.0 mm is filled with helium under a pressure p =
= 1.0 Pa. One plate is kept at a temperature ti = 17 °C and the
other, at a temperature t 2 = 37 °C. Find the mean free path of helium
atoms and the heat flow density.