(a) for the solidification of iron, calculate the critical radius r* and the activation free energy δg* if nucleation is homogeneous. values for the latent heat of fusion and surface free energy are –1.85 × 109 j/m3 and 0.204 j/m2, respectively. use the supercooling value δt = 273 k, and the melting point of iron is 1538°c.

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)?