Question

P2-44 A piston-cylinder assembly of total mass 16 lbm is free to move within a housing. Initially the cylinder contains gas at an absolute pressure of 20 Ibf/in^2 and a volume of 0.07 ft^3 and is at rest. The piston is then moved so that the entire assembly accelerates rightward and reaches a final velocity of 7.5 ft/s. During this process, the gas is compressed to a final pressure of 35 Ibf/in^2 The process is adiabatic, and the pressure is related to the volume by PV^1.4= constant. Calculate the change in internal energy for this process in Btu.

Answer 1

Given data for the process:  

Initial pressure = 20 lbf/in^2        

initial volume = 0.07 ft^3    = 120.96 inch^3               (1 ft^3 = 1728 inch^3 )

Final pressure = 35 lbf/in^2         

process is adiabatic, For adibatic pressure

For adiabatic process, Workdone

or Work in the said process ( in unit of lbf-ft)

From First Law of thermodynamics,

dQ = 0   in this case of adiabatic process

dU = Change in internal energy

dW = work interaction in the process

therefore dU = change in internal energy for the process is

So internal energy of the system will increases by +87.3833 lbf-ft

Now , we know that   1 Btu = 778.16 lbf-ft

Hence

internal energy of the system will increases by 0.11229 Btu.