Problem 1: An ideal gas with constant specill undergoes an expansion in a steady-flow machine with a mass flow rate of 100 lbm/hr. The machine is water-cooled. The water mass flow rate is 10 Ibm/hr. The gas temperature drops, during the process, from 200 to 100°F, and the water temperature rises from 70 to 100°F. The specific heat of the water is cp 1.0 BTU/Ibm °R. Determine the work done by the gas in BTU/hr and W. Problem 2: An ideal gas with constant specific heats (cp = 0.25 BTU/lbm-°R, c₁ = 0.184 BTU/lbm °R, R = 0.06618 BTU/lbm °R) undergoes a nonflow polytropic compression during which the temperature rises from 100 to 200°F. The polytropic exponent is 1.3. Calculate the work done and the heat transfer in BTU/lbm. Problem 3: A 10-m³ rigid tank contains steam at 30 bar and 400°C. It is left to cool down until its pressure drops to 5 bar. Find (a) the final state of the steam, and (b) the heat transfer, in kJ. Problem 4: An inventor claims to have built an engine that operates on a cycle, receives 1000 kJ at 500°C, produces work, and rejects 350 kJ at 50°C. Is this claim valid? Why? Problem 5: Air expands from 10 bar and 1000°C to 1 bar and 500°C in an insulated turbine. Calculate (a) the turbine's isentropic efficiency, (b) the change in entropy of the air, in kJ/kg-K, (c) the work, in kJ/kg, and (d) the polytropic exponent, n. Assume the air has constant specific heats, with cp = 1.005 kJ/kg.K. Problem 6: 1000 kg/hr of water at 60°C and 1 bar are pumped to 100 bar. The pump efficiency is 0.65. Find the work in kW.