:A gas contained in a piston-cylinder assembly undergoes two processes, A and B, between the same end states, 1 and 2, where p1 =1bar, V1 = 1m3 , U1 =400kJ and p2 = 10 bar, V2 = 0.1 m3 , U2 = 450 kJ: Process A: Constant- volume process from state 1 to a pressure of 10 bar, followed by a constantpressure process to state 2. Process B: Process from 1 to 2 during which the pressure-volume relation is pV = constant. Kinetic and potential %3D effects can be ignored. For each of the processes A and B, (a) sketch the process on p-V coordinates, (b) evaluate the work, in kJ, and (c) evaluate the heat transfer, in kJ.
: A gas contained in a piston–cylinder assembly undergoes two processes, A and B, between the same end states, 1 and 2, where p1 =1bar, V1 = 1m3 , U1 =400kJ and p2 = 10 bar, V2 = 0.1 m3 , U2 = 450 kJ: Process A: Constant-volume process from state 1 to a pressure of 10 bar, followed by a constantpressure process to state 2. Process B: Process from 1 to 2 during which the pressure-volume relation is pV = constant. Kinetic and potential effects can be ignored. For each of the processes A and B, (a) sketch the process on p–V coordinates, (b) evaluate the work, in kJ, and (c) evaluate the heat transfer , in kJ.
Given,
P1= 1 bar=1*102 kPa, P2= 10 bar= 10*102 kPa,
V1= 1 m3, V2= 0.1 m3,
U1= 400 kJ, U2= 450kJ.
Process A : Constant-volume process from state 1 to a pressure of 10 bar, followed by a constant pressure process to state 2.
Process B : Process from 1 to 2 during which the pressure-volume relation is PV=constant.
b) Work for process A will be
WA = P1dV + P2dV
WA = 1 * 102 * (V2-V1) + 10 * 102 * (V2-V1)
= 100 ( 1 - 1 ) +1000 ( 0.1 - 1 )
WA = -900 kJ
The negative sign represents work done on the system.
Work for process B will be
WB = Work done for iso-thermal process
WB = P1 * V1 * ln (V2/V1)
= 1 * 102 * ln (0.1/1)
WB = -230.3 kJ
c) Heat = Change in internal energy + work done
Change in internal energy = 450 - 400 = 50 kJ
Heat for process A will be,
ΔHA = ΔU + WA
= 50 - 900
ΔHA = -850 kJ
The negative sign represents the heat is given to the system.
Heat for process b will be
HB = WB
HB = -230.3 kJ .....because the change in internal energy is zero for iso-thermal process.
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