A chemical engineer claims to have devised a closed device, operating isothermally at 300 K, that could expand 100 mol of methane (assumed to be an ideal gas) from 1.0 to 0.4 MPa, and in the process generate 250 kJ of useful work. Should we believe this claim? Answer the question by calculating the change in entropy of the system, the change in entropy of the surroundings, and the total change in entropy of the universe.

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)?