# Calculating Thermal Wavelength

For O2(g) in a 200mL container at 1500K, calculate q(trans) and the thermal wavelength.

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#### Solution Preview

q(trans) = (2*pi*m*k*T/h^2)^(3/2)*V

m = 32*1.67*10^(-27) kg = mass of molecule

k = 1.38*10^(-23) J/molecule/k

T = 1500 K

h = ...

#### Solution Summary

Solution provides calculations and the answer. The thermal wavelengths are calculated.

Scattering Mechanism in Metals

Consider the thermal conductivity K of a pure synthetic sapphire crystal that has a diameter of 3mm. (For sapphire delta D -1000 K , speed of sound - 10^4ms^-1, and for T <<delta D, cv - 10^-1 T^8 J M K^-1, delta D is the Debye temperature and T is the temperature).

a. Discuss which scattering mechanism dominates the thermal conductivity K of the sapphire crystal at 20 k

b. Discuss which scattering mechanism dominates the thermal conductivity K of the sapphire crystal at 1000 K.

c. Given that K - 1/3 c, vl where Cv is the specific heat capacity per unit volume, v is the speed of sound and l is the mean free path, and that the thermal conductivity K reaches a sharp maximum at a temperature of 30 K, estimate the maximum value of K.

d. Sketch K versus T for the temperature range 2K to 100 K.

See attachment for better formula representation.

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