A piston -cylinder assembly fitted with a paddle...

A piston -cylinder assembly fitted with a paddle wheel contains, air, initially at P1= 50Lbf/in², T1= 540F and V1=4ft³. The air undergoes a process to a final state where P2= 20Lbf/in², V2=9ft³. During the process, the paddle wheel transfer energy TO the air by work in the amount 10Btu, while the air transfers energy by work TO the piston in the amount 14Btu. Assuming ideal gas behavior, calculate for air (a) Mass (b) Temperature final sate Heat transfer, in Btu.

Transcript

00:02 A piston cylinder device contains air and a paddle wheel supplies a given amount of work to the air.

00:09 We want to calculate the heat transfer in this problem.

00:13 So we make a assumption that air is an ideal gas.

00:16 The kinetic and potential energy changes are negligible and we can use constant specific heats for air.

00:23 So the first thing we will do is take the air as a closed system since no mass enters or leaves the system.

00:29 So the energy balance equation is e in minus e out is equal to delta e for the system.

00:36 So the change in energy is equal to e in minus e out.

00:41 And the net energy transfer into the system is firstly due to the paddle wheel.

00:49 So this equation becomes the work done by the paddle wheel minus the boundary work out of the system, a minus for the work out, plus the heat which is added into the system must be equal to the change in internal energy delta u and delta u is equal to the mass of a times the specific heat capacity cv times a change in temperature t2 minus t1 now t1 is equal to t2 so basically what we have is that since the temperature does not change the work done by the paddle wheel minus the boundary work out of the system plus the heat into the system must equal to zero so remember the temperature is left to remain constant so t2 equals to t1 and so we can write this as the heat transfer is equal to the boundary work out of the system minus the work done by the pedal wheel into the system.

02:23 So now we have our energy balance equation.

02:27 We can, we first need to find this boundary work so that we can calculate this heat transfer...

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