The current through a 20.0-mH inductor is LaTeX: i(t)=8t\exp(-t/5) i ( t ) = 8 t exp ⁡ ( − t / 5 ) for LaTeX: t\geq0 t ≥ 0 , where LaTeX: t t is given in seconds and LaTeX: i(t) i ( t ) is given in mA. What is the magnitude of the induced emf across the inductor when LaTeX: t=3.0~\mathrm{s} t = 3.0 s ?

Amass of 1.5 kg of air at 120 kpa and 24°c is contained in a gas-tight, frictionless piston-cylinder device. the air is now compressed to a final pressure of 720 kpa. during the process, heat is transferred from the air such that the temperature inside the cylinder remains constant. calculate the boundary work input during this process.

Avolume of 2.65 m3 of air in a rigid, insulated container fitted with a paddle wheel is initially at 264 k, 5.6 bar. the air receives 432 kj by work from the paddle wheel. assuming the ideal gas model with cv = 0.71 kj/kg • k, determine for the air the amount of entropy produced, in kj/k

A3-mm-thick panel of aluminum alloy (k 177 w/m-k, c 875 j/kg-k and ? = 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above t,-150°c for at least 5 min. the production line for the curing operation involves two steps: (1) heating in a large oven with air at ts,0-175°c and a convection coefficient of h, 40 w/m2. k, and (2) cooling in a large chamber with air at 25°c and a con- vection coefficient of he 10 w/m2.k. the heating portion of the process is conducted over a time interval te which exceeds the ime required to reach 150°c by 5 min (h = r + 300 s). the coating has an emissivity of ? = 0.8, and the temperatures of the oven and chamber walls are 175 and 25°c, respectively. if the panel is placed in the oven at an initial temperature of 25°c and removed from the chamber at a safe-to-touch tempera ture of 37°c, what is the total elapsed time for the two-step curing operation?