Question 3 a) A frictionless piston-cylinder device contains an ideal gas initially at P., T, and V,. The gas is then heated until it reaches a temperature of T2. Show that the final volume, V, is...

Extracted text: Question 3 a) A frictionless piston-cylinder device contains an ideal gas initially at P., T, and V,. The gas is then heated until it reaches a temperature of T2. Show that the final volume, V, is given by the following equation V2 T2 = T V1 (2 marks) b) A frictionless piston cylinder device contains 2.5 liter of air initially at 100 kPa and 37°C. The air undergoes several thermodynamic processes as follows: 1-2: isothermal compression process until the volume is reduced to 10% of the initial volume; 2-3: isobaric expansion process until the volume reaches the initial volume; and 3-1: isochoric cooling process until the initial state is reached. Determine i. the mass of air (kg); ii. the pressure at state 2 (kPa); iii. the change in volume of the expansion process 2-3 (m³); iv. the temperature at state 3 (K); and sketch the processes on a P-V diagram. v. Take for air, R = 0.2870 kJ/kg.K. Unit conversion:1 liter = 0.001 m'; T(K) = T(°C) + 273 (8 marks)