What is the expression for the change in Gibbs Free Energy as a function of critical magnetic field(Hc) if its temperature dependence is given by Hc =Ho(1-T/Tc).

(a) Consider nodal configuration shown below. (a) Derive the finite-difference equations under steady-state conditions if the boundary is insulated. (b) Find the value of Tmn if you know that Tm, n+1= 12 °C, Tm, n-1 = 8 °C, Tm-1, n = 10 °C, Ax = Ay = 10 mm, and k = W 3 m. k Av m-1.n 1 m, n-1 The side insulated

A Maxwell-Boltzmann distribution implies that a given molecule (mass m ) will have a speed between 1 and v + dv with probability equal to f(v)dv where ƒ(v) ∞ v² e-mv²/2k³I and the proportionality sign is used because a normalization constant has f(v)dv.) For this distribution, calculate the been omitted. (You can correct for this by dividing any averages you work out by mean speed (v) and the mean inverse speed (1/v). Show that (v)(1/v) = ¼/ .

9.1. Consider the results for ideal gases derived from quantum mechanics. Write an expression for the function s(T, v) that includes the parameter A(T). (a) Show that the behavior of the entropy as T0 is unrealistic in a quantum sense. What approximation in the derivation is responsible for this behavior? (b) The Sackur-Tetrode equation is valid when the thermal de Broglie wave- length is much less than the average molecular separation distance, A(T) < (V/N)13, which is generally the case at high temperatures. Calculate the temperature at which this inequality is first violated for an ideal gas at atmospheric pressure and with a mass of 6.6 × 10-26 kg/molecule (which is typical of argon). x

7.7 The measured thermal conductivity of germanium at 300°K is 0.63 W/°K, in a range where acoustic phonon scattering dominates. (a) What fraction of this thermal conductivity is caused by free electrons if the free-electron density is 1017 cm-³ and the electron mobility is 4x 10 cm2/V-sec? (b) What must the concentration of free electrons in germanium at 300°K be in order for the electronic contribution to the thermal conductivity to be equal to the lattice contribution? (c) The thermoelectric power corresponding to (a) is measured to be 0.46 mV/°K. How far below the conduction-band edge does the Fermi level lie?

Show that for an ideal gas (@T/ƏV)u = 0, and (@T/ƏP)H= 0.

Use the experimental value of the coefficient of viscosity for nitrogen (Table 16A.1) to estimate the collision cross-section of the molecules at 273 K.

The variation of the molar Gibbs free pn- ergy of a substance with temperature and pressure is given by () T5/2 G = -T In Determine S, H, V, U and F.

Consider a system with 1000 particles that can only have two energies, ɛ, and with ɛ, > E,. The difference between these two values is Aɛ = ɛ, -& . Assume that gi = g2 = 1. Using the %3D %3D equation for the Boltzmann distribution graph the number of particles, ni and m, in states & n2, E and E, as a function of temperature for a Aɛ = 1×10-2' J and for a temperature range from 2 to 300 K. (Note: kg = 1.380x10-23 J K-!. %3D %3D (s,-s,) gLe Aɛ/ n2 or = e n,

The Z factor is approximately the same for all gases at the same reduced temperature and reduced pressure.