please give me answers for all questions .

(02) (a) Show that the general expression for the work done during a polytropic process (i.e. PVn= Constant) in a typical piston cylinder device containing an ideal gas is given by W=1nP2V2P1V1 where P,V, and T are pressure, volume and temperature, respectively. [05 marks] (b) A piston-cylinder device contains 1.2kg of nitrogen gas at 120kPa and 27C. The gas is now compressed slowly in a polytropic process during which PV1.3= constant. The process ends when the volume is reduced by one-half. Data: Nitrogen is an ideal gas with C=1.040kJ/kgK and Cv=0.743kJ/kgK. i. Calculate the pressure and temperature at the end of the process. [04 marks] ii. Determine the internal energy change and enthalpy change of nitrogen during the process. [04 marks] iii. Calculate the total work transfer during the process. [03 marks] iv. Determine the entropy change of nitrogen during the process. [04 marks] Gibbs Equations: TdS=dU+PdV;TdS=dHVdP Ideal Gas: RG=CCv;k=C/Cv (03) (a) Define "the increase of entropy principle" and explain how it can be used to determine the direction of a process. [05 marks] (b) A10kg iron block initially at 350C is dropped into an insulated tank that contains 100kg of water at 30C. The average specific heat capacity of water and iron is Cp, water =4.18kJ/kgC, and C, iron =0.45kJ/kgC, respectively. i. Determine the final equilibrium temperature. [05 marks] ii. Determine the total entropy change during this process. [07 marks] iii. Check whether the process is reversible or irreversible. [03 marks] ]