Determine for what energy above EF (in terms of kT ) the Fermi–Dirac probability function is within 1 percent of the Boltzmann approximation. (b) Give the value of the probability function at this energy.

Asolid cylinder is concentric with a straight pipe. the cylinder is 0.5 m long and has an outside diameter of 8 cm. the pipe has an inside diameter of 8.5 cm. the annulus between the cylinder ad the pipe contains stationary oil. the oil has a specific gravity of 0.92 and a kinematic viscosity of 5.57 x 10-4 m2/s. most nearly, what is the force needed to move the cylinder along the pipe at a constant velocity of 1 m/s?

1in2 processor chip can be modelled as an isothermal plane wall of silicon, isothermal on both sides. the power input to the bottom of the plane wall, or the processing power of the chip, often called the thermal design power (tdp), is 100w. assume the periphery is adiabatic. the silicon is 400 microns thick. the temperature at the junction, or in this case on the bottom of the isothermal plane wall, is 85°c. what is the top surface temperature, assuming that the only mode of heat transfer is conduction

Asolid steel sphere (k=63.9 w m-1 k-1 , ? =7832 kg m-3 , c=0.523 kj kg-1 k-1 ), 100 mm in diameter is initially at a uniform temperature of 500o c and is suddenly quenched in a large oil bath for which t? = 100o c and h = 3200 w m-2 k-1. estimate the time required for the sphere to cool to 200o c and to 110o c