Radioactive wastes (k_rw = 20 W/m K) are stored in a spherical, stainless steel (k_ss = 15 W/m K) container of inner and outer radii equal to r_i = 0.6 m and r_0 = 0.7 m. Heat is generated volumetrically within the wastes at a uniform rate of q = 10^5 W/m^3, and the outer surface of the container is exposed to a water flow for which he = 1000 W/m^2 K and T_infinity = 25 degrees C.
Evaluate the steady-state inner surface temperature, T_s, o. Evaluate the steady-state inner surface temperature, T_s, i.
Obtain an expression for the temperature distribution, T(r), in the radioactive wastes. Express your result in terms of r_i, T_s, i, k_rw, and q.
Evaluate i temperature at r = 0.

Prove the equivalence between the two statements of the 2nd law of thermodynamics (i.e., a violation of one statement leads to the violatio the other statement)

Water vapor initially at 10 bar and 400 °c is contained within a piston-cylinder assembly. the water lost heat to the surrounding according to isochoric (iso-volumetric) process until its temperature is 150 °c. the water is then condensed isothermally to saturated liquid. for the water as a system, calculate the work in kj/kg

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?