Assignment 3 First Law Closed System 1 A 4-m x 5-m x 7-m room is heated by the radiator of a steam-heating system. The steam radiator transfers heat at a rate of 10,000 kJ/h, and a 100-W fan is used to distribute the warm air in the room. The rate of heat loss from the room is estimated to be about 5000 kJ/h. If the initial temperature of the room air is 10C, determine how long it will take for the air temperature to rise to 20C. Assume local atmospheric pressure as 100kPa and air has constant specific heats C,-0.718kJ/kg.K and gas constant of R=0.287 kPa.m/kg.K. Answers: 831 seconds 2 Air is contained in a piston-cylinder device at 600 kPa and 927 C, and occupies a volume of 0.8 m. The air undergoes and isothermal (constant temperature) process until the pressure in reduced to 300 kPa. The piston is now fixed in place and not allowed to move while a heat transfer process takes place until the air reaches 27C. (a) Sketch the system showing the energies crossing the boundary and the P-V diagram for the combined processes. (b) For the combined processes determine the net amount of heat transfer, in kJ, and its direction. Assume air has constant specific heats Cv=0.718kJ/kg.K and gas constant of R=0.287 kPa.m/kg.K. Answers: (b) Qout = 568kJ 3 A piston-cylinder device contains 2.2 kg of nitrogen initially at 100 kPa and 25C. The nitrogen is now compressed slowly in a polytropic process during which PV=constant until the volume is reduced by one-half. Determine the work done and the heat transfer for this process. The gas constant of N2 is R = 0.2968 kPa.m/kg.K and the Cv=0.744 kJ/kg.K. Answers: Work done=149.9kJ & Heat transfer=37.2kJ 4 An insulated piston-cylinder device initially contains 1.8-kg saturated liquid water at 120C. Now an electric resistor placed in the tank is turned on for 10 min until the volume quadruples. Determine (a) the volume of the tank, (b) the final temperature, and (c) the electrical power rating of the resistor. Answers: (a) 0.00763 m, (b) 120C, (c) 0.0236 kW 5 A mass of 3 kg of saturated liquid-vapor mixture of water is contained in a piston-cylinder device at 160 kPa. Initially, 1 kg of the water is in the liquid phase and the rest is in the vapor phase. Heat is now transferred to the water, and the piston, which is resting on a set of stops, starts moving when the pressure inside reaches 500 kPa. Heat transfer continues until the total volume increases by 20 percent. Determine (a) the initial and final temperatures, (b) the mass of liquid water when the piston first starts moving, and (c) the work done during this process. Also, show the process on a P-v diagram. Answers: (a) T1=113.3 C & T2=675 C and, (b) 0.728m/kg, (c) 218 kJ