Problems and Solutions on Thermodynamics and Statistical Mechanics

367 SOLVED PROBLEMS

Question: 2.165

Radiation pressure. One may think of radiation as a gas of photons and apply many of the results from kinetic theory and thermodynamics to the radiation gas. (a) Prove that the pressure exerted by an isotropic radiation field of energy density u on a perfectly reflecting wall is p = u/3. ...

(a) Consider an area element dS of the perfectly r...
Question: 2.163

A system consists of N very weakly interacting particles at a temperature sufficiently high such that classical statistics are applicable. Each particle has mass m and oscillates in one direction about its equilibrium position. Calculate the heat capacity at temperature T in each of the following ...

According to the virial theorem, if the potential ...
Question: 2.162

Starting with the virial theorem for an equilibrium configuration show that: (a) the total kinetic energy of a finite gaseous configuration is equal to the total internal energy if γ = Cp /Cv = 5/3 , where Cp and Cv are the molar specific heats of the gas at constant pressure and at constant volume ...

For a finite gaseous configuration, the virial the...
Question: 2.161

A box of volume 2V is divided into halves by a thin partition. The left side contains a perfect gas at pressure p0 and the right side is initially vacuum. A small hole of area A is punched in the partition. What is the pressure p 1 in the left hand side as a function of time? Assume the temperature ...

Because the hole is small, we can assume the gases...
Question: 2.166

A gas of interacting atoms has an equation of state and heat capacity at constant volume given by the expressions p(T,V )= aT^1/2 + bT^3 + c V ^- 2, Cv(T, V)= dT^1/2V + eT^2V + fT^1/2, where a through f are constants which are independent of T and V . (a) Find the differential of the internal ...

\text { (a) We have } d U(T, V)=C_{v} d T+\...
Question: 2.169

(a) Assuming moderately dilute helium gas so that binary collisions of helium atoms determine the transport coefficients] derive an expression for the thermal conductivity of the gas. (b) Estimate the ratio of the thermal conductivity of gaseous ^3He to that of gaseous ^4He at room temperature. ...

(a) Consider an area element dS of an imaginary pl...
Question: 2.170

A certain closed cell foam used as an insulating material in houses is manufactured in such a way that the cells are initially filled with a polyatomic gas of molecular weight ∼60. After several years the gas diffuses out of the foam and is replaced by dry air (mean molecular weight ...

The thermal conductivity is \kappa \sim \la...
Question: 2.171

Thermos Bottle. (a) State and justify how the thermal conductivity of an ideal gas depends on its density at fixed temperature. (b) A thermos (Dewar) bottle is constructed of two concentric glass vessels with the air in the intervening space reduced to a low density. Why can it act as an insulating ...

(a) The mean speed of the air molecules is constan...
Question: 2.172

Sketch the temperature dependence of the heat conductivity of an insulating solid. State the simple temperature dependencies in limiting temperature ranges and dervie them quantitatively. ...

The thermal conductivity of a solid is \kap...
(a) The coefficient of viscosity is \eta=\f...