TUTORIAL 1

Constant Volume Process V = constant cv(T2-T1) q= cv(T2-T1) Summary of closed system processes for gases Wother=0; cp – cv = R; k = cp/cv Name Law Wb (kJ/kg) ∆u (kJ/kg) q = wb + ∆u (kJ/kg) Constant Volume Process V = constant cv(T2-T1) q= cv(T2-T1) Constant Pressure process P = constant R(T2-T1) q= cp(T2-T1) Constant Temp. (Isothermal) Process T = constant RTln(v2/v1) Polytropic Process Pvn = constant R(T1 –T2)/(n-1) (k-n)/(k-1)*R(T1 –T2)/(n-1) Adiabatic Process Pvk = constant R(T1 –T2)/(k-1)

Problem 1. Each line in the table below gives information about a process of a closed system. Every entry has the same energy units. Fill in the blank spaces with the appropriate values. Process Q W E1 E2 ∆E A -20 20 70 B 50 10 60

Problem 2. An ideal gas is contained in a closed assembly with an initial pressure and temperature of 220 kPa and 70 deg C, respectively. If the volume of the system is increased 1.5 times and the temperature drops to 15 deg C, determine the final pressure of the gas.

Problem 3. In the compression stroke of an internal combustion engine the work input is 70 kJ/kg and the heat rejected to the cooling water is 25 kJ/kg. Calculate the change in internal energy per unit mass of the working fluid. State whether it is a gain or a loss. Neglect the change in kinetic and potential energies. Problem 4. 4.5 kg of steam in a piston-cylinder assembly is subjected to an input work by the paddle wheel of 20.5 kJ while 60 kJ of heat is added. The system initial internal energy is 2710 kJ/kg and is 2660 kJ/kg after the expansion process. Determine the amount of energy transfer by work from the steam to the piston. Neglect the change in kinetic and potential energy.

Problem 5. 10 kg of gas in a piston-cylinder assembly undergoes a process for which The gas is initially at 3 bars and 0.1 m3 and its final pressure is 0.2 m3. The change in the internal energy is -7.4 kJ/kg and there is no significant change in its kinetic and potential energy. Determine the net heat transfer during the process. Problem 6. A working fluid in an engine undergoes a cycle in three processes in series. During the first process, 15 kJ of work is done on the fluid with 60 kJ of heat rejected. During the second process, the working fluid produces 44 kJ of work while receiving 36 kJ of heat. During the third process the working fluid is brought back to the initial state with only heat transfer. Determine the heat transfer during the final process.

Problem 7. A piston-cylinder device contains 2 kg of gas Problem 7. A piston-cylinder device contains 2 kg of gas. The gas undergoes a thermodynamic cycle with three processes as follows: Process 1-2: constant pressure expansion at 1.4 bar, V1 = 0.028 m3, W = 10.5 kJ Process 2-3: isothermal compression, U2 = U3 Process 3-1: constant volume with U1 – U3 = -26.4 kJ. Plot the cycle on the p-V diagram and determine (a) the net work done in the cycle in kJ, and (b) heat transfer during process 1-2 in kJ.

Problem 8. A mass of gas occupying 0 Problem 8. A mass of gas occupying 0.08 m3 at 6 kN/m2 and 80 deg C is expanded reversibly by the law pV1.2 = constant. The pressure at the end of expansion is 0.7 kN/m2. The gas is then heated at constant pressure to the original temperature. The specific heat capacities at constant pressure and constant volume are 1.00 and 0.74 kJ/kg K respectively. Determine (a) the work transfer in the expansion process, (b) the heat transfer in the expansion process, (c) the volume at the end of the heating process, and (d) the change in internal energy during the heating process. Problem 9. A reciprocating compressor delivers 0.1 kg/s of compressed air at a pressure of 12 bar following a reversible polytropic compression, pv1.2 = Constant. The air enters the compressor at a pressure of 1 bar and a temperature of 15 deg C. Calculate the delivery temperature of the air, the work transfer rate and the heat transfer rate in the above compression process. Air may be treated as a perfect gas for which the specific heat capacity at constant pressure, cp = 1.005 kJ/kg K and k = 1.4.