H2s 344j6p

PROBLEM 2.31

Problem 2.31 (Cont’d)

Problem 2.34 Carbon monoxide gas (CO) contained within a piston-cylinder assembly undergoes three processes in series: Process 1-2: Constant pressure expansion at 5 bar from V1 = 0.2 m3 to V2 = 1 m3. Process 2-3: Constant volume cooling from state 2 to state 3 where p3 = 1 bar. Process 3-1: Compression from state 3 to the initial state during which the pressure-volume relationship is pV = constant. Sketch the processes in series on p-V coordinates and evaluate the work for each process, in kJ. KNOWN: Carbon monoxide gas within a piston-cylinder assembly undergoes three processes in series. FIND: Sketch the processes in series on a p-V diagram and evaluate the work for each process. SCHEMATIC AND GIVEN DATA:

p (bar)

CO 5 Process 1-2: Constant pressure expansion at 5 bar from V1 = 0.2 m3 to V2 = 1 m3. Process 2-3: Constant volume cooling from state 2 to state 3 where p3 = 1 bar. Process 3-1: Compression from state 3 to the initial state during which the pressure-volume relationship is pV = constant.

1

1

2

3

pV = constant

0.2

1

ENGINEERING MODEL: (1) The gas is the closed system. (2) Volume change is the only work mode. (3) Each of the three processes is specified. ANALYSIS: Since volume change is the only work mode, Eq. 2.17 applies. Process 1-2: Constant pressure processes: (out) Process 2-3: Constant volume (piston does not move). Thus W23 = 0

V (m3)

Problem 2.33 (Continued) Process 3-1: For process 3-1, pV = constant = p1V1 . Noting that V3 = V2, we get

Inserting values and converting units 1

= -160.9 kJ (in)

1. The net work for the three process is Wnet = W12 + W23 + W31 = (+400) + 0 + (-160.9) = 239.1 kJ (net work is positive - out)

Problem 2.35 Air contained within a piston-cylinder assembly undergoes three processes in series: Process 1-2: Compression during which the pressure-volume relationship is pV = constant from p1 = 10 lbf/in.2, V1 = 4 ft3 to p2 = 50 lbf/in.2 Process 2-3: Constant volume from state 2 to state 3 where p = 10 lbf/in.2 Process 3-1: Constant pressure expansion to the initial state. Sketch the processes in series on a p-V diagram. Evaluate (a) the volume at state 2, in ft3, and (b) the work for each process, in Btu. KNOWN: Air within a piston-cylinder assembly undergoes three processes in series. FIND: Sketch the processes in series on a p-V diagram. Evaluate (a) the volume at state 2, and (b) the work for each process. SCHEMATIC AND GIVEN DATA: p

2

Air pV = constant Process 1-2: Compression during which the pressure-volume relationship is pV = constant from p1 = 10 lbf/in.2, V1 = 4 ft3 to p2 = 50 lbf/in.2 Process 2-3: Constant volume from state 2 to state 3 where p = 10 lbf/in.2 Process 3-1: Constant pressure expansion to the initial state.

3

ENGINEERING MODEL: (1) The gas is the closed system. (2) Volume change is the only work mode. (3) Each of the three processes is specified. ANALYSIS: (a) For process 1-2; pV = constant. Thus p1V1 = p2V2, and = 0.8 ft3 (b) Since volume change is the only work mode, Eq. 2.17 applies. Process 1-2: For process 1-2, pV = constant = p1V1 . Thus

1 V

Problem 2.35 (Continued) Inserting values and converting units = -11.92 Btu (in)

Process 2-3: Constant volume (piston does not move). Thus W23 = 0 Process 3-1: Constant pressure processes (p3 = p1): Noting that V3 = V2 = 5.92 Btu (out)

1. The net work for the three process is Wnet = W12 + W23 + W31 = (-11.92) + 0 + (5.92)) = - 6 kJ (net work is negative - in)

PROBLEM 2.59

PROBLEM 2.60