The inlet to a nitrogen compressor is a pipe of 5cm internal diameter; its outlet is a pipe of 2 cm internal diameter. At steady state, the temperature at the inlet is T(in) = 300k. pressure Pin = 10 bar, the flow rate of N2 is 5 mol/s, pressure at the outlet is Pout = 100 bar. And the compressor uses 45 kW of electrical power. Heat losses are negligible. Estimate the temperature at which the outlet of the compressor: (a) assuming N2 is an ideal gas with constant heat capacity, Cv = 5R/2. and (b) using accurate thermodynamic data for N2.