When the conduction electrons in a metal are treated as an ideal gas of fermions, the mean number of electrons occupying a state with energy e is given by i+ (-2) (3)u (a) define the fermi energy [ marks] (b) sketch n as a function of e for an electron gas: (i) at t 0 k, and to the fermi temperature (ii) at a temperature above 0 k, but small compared label and briefly justify each sketch [5 marks] (c) describe the change in the variation of n with e as the temperature increases, and hence explain why conduction electrons make only a small contribution to the heat capacity of a metal at room temperature

Steam is generated in a boiler of a cogeneration plant at 10 mpa and 450°c at a steady rate of 5 kg/s. in normal operation, steam expands in a turbine to a pressure of 0.5 mpa and is then routed to the process heater, where it supplies the process heat. steam leaves the process heater as a saturated liquid and is pumped to the boiler pressure. in this mode, no steam passes through a condenser, which operates at 20 kpa. (a) determine the power produced in the turbine and the rate at which process heat is supplied in this mode. (b) determine the power produced in the turbine and the rate of process heat supplied if only 60 percent of the steam is routed to the process heater and the remainder is expanded to the condenser pressure. (3.32 mw; 9.69 mw; 4.25 mw; 5.82 mw)