Hooke's law describes an ideal spring. Many real springs are better described by the restoring force (F Sp ) s =−kΔs−q(Δs) 3 (p)s=−kΔs−q(Δs)3 , where q q is a constant. Consider a spring with k kk = 350 N/m N/m and q qq = 750 N/m 3 N/m3 .How much work must you do to compress this spring 15cm? Note that, by Newton's third law, the work you do on the spring is the negative of the work done by the spring. By what percent has the cubic term increased the work over what would be needed to compress an ideal spring?

As part of an industrial process, air as an ideal gas at 10 bar, 400k expands at steady state through a valve to a pressure of 4 bar. the mass flow rate of air is 0.5 kg/s. the air then passes through a heat exchanger where it is cooled to a temperature of 295k with negligible change in pressure. the valve can be modeled as a throttling process, and kinetic and potential energy effects can be neglected. (a) for a control volume enclosing the valve and heat exchanger and enough of the local surroundings that the heat transfer occurs at the ambient temperature of 295 k, determine the rate of entropy production, in kw/k. (b) if the expansion valve were replaced by an adiabatic turbine operating isentropically, what would be the entropy production? compare the results of parts (a) and (b) and discuss.