An air pump is used to fill a rigid gas bottle with air. The pump is connected to the gas bottle via a rigid pipe. The pump consists of a piston of internal diameter d=0.08 m and a cylinder with a stroke L=0.3m. Air enters the pump through an orifice located at the bottom of the cylinder to raise the pressure in the pump to atmospheric pressure. Air, drawn into the pump through the orifice, mixes completely and adiabatically with the cylinder contents. A valve allows the bottle's refill. The valve opens when the pump pressure is equal to the gas bottle. The valve is always closed when the pump pressure is below the gas bottle pressure. Pressure drop across the valve can be neglected. The bottle, the connecting pipe and the pump are thermally insulated. Air in the pump and connecting pipe undergoes isentropic compression and expansion processes. F-one The working fluid (air) can be considered a perfect gas with R=287 J/KgK, cp=1005 J/KgK and y=1.4. Initially the piston is located at the bottom of the cylinder, the valve is open and pressure and temperature are 1bar and 298K in the pump, the bottle and the surrounding ambient air. Air transferring to the gas bottle mixes completely and adiabatically on entering. Determine: 6) Plot a pressure versus volume diagram for air in the cylinder and connecting pipe for the first cycle.

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An air pump is used to fill a rigid gas bottle with air. The pump is connected to the gas
bottle via a rigid pipe. The pump consists of a piston of
internal diameter d=0.08 m and a cylinder with a stroke
L=0.3m. Air enters the pump through an orifice located at the
bottom of the cylinder to raise the pressure in the pump to
atmospheric pressure. Air, drawn into the pump through the
orifice, mixes completely and adiabatically with the cylinder
contents. A valve allows the bottle's refill. The valve opens
when the pump pressure is equal to the gas bottle. The valve
is always closed when the pump pressure is below the gas
bottle pressure. Pressure drop across the valve can be
neglected. The bottle, the connecting pipe and the pump are thermally insulated. Air in
the pump and connecting pipe undergoes isentropic compression and expansion processes.
I
F-one
The working fluid (air) can be considered a perfect gas with R=287 J/KgK, cp=1005 J/KgK
and y=1.4. Initially the piston is located at the bottom of the cylinder, the valve is open
and pressure and temperature are 1bar and 298K in the pump, the bottle and the
surrounding ambient air.
Air transferring to the gas bottle mixes completely and adiabatically on entering.
Determine:
6) Plot a pressure versus volume diagram for air in the cylinder and connecting pipe
for the first cycle.
Transcribed Image Text:An air pump is used to fill a rigid gas bottle with air. The pump is connected to the gas bottle via a rigid pipe. The pump consists of a piston of internal diameter d=0.08 m and a cylinder with a stroke L=0.3m. Air enters the pump through an orifice located at the bottom of the cylinder to raise the pressure in the pump to atmospheric pressure. Air, drawn into the pump through the orifice, mixes completely and adiabatically with the cylinder contents. A valve allows the bottle's refill. The valve opens when the pump pressure is equal to the gas bottle. The valve is always closed when the pump pressure is below the gas bottle pressure. Pressure drop across the valve can be neglected. The bottle, the connecting pipe and the pump are thermally insulated. Air in the pump and connecting pipe undergoes isentropic compression and expansion processes. I F-one The working fluid (air) can be considered a perfect gas with R=287 J/KgK, cp=1005 J/KgK and y=1.4. Initially the piston is located at the bottom of the cylinder, the valve is open and pressure and temperature are 1bar and 298K in the pump, the bottle and the surrounding ambient air. Air transferring to the gas bottle mixes completely and adiabatically on entering. Determine: 6) Plot a pressure versus volume diagram for air in the cylinder and connecting pipe for the first cycle.
Notes:
a)
b)
c)
A simplified sketch of the thermodynamic system showing cylinder/piston
at initial conditions can be represented as:
Gas bottle
Valve
Cylinder
L=0.3m; d = 0.08m Vp/Vc=0.1 and Vb/Vc=0.9
Where V₂= connecting pipe volume, Vc= pump cylinder volume, V₁= bottle volume
First cycle of the pump comprises:
First compression 1-2: Isentropic compression (valve is open; initial
volume being Vc+Vb+Vp)
First expansion 2-3: Isentropic expansion. Bottle valve closed
Filling of pump and connecting pipe 3-4. Adiabatic
Cylinder
Orifice
To solve point 5 you would need the following result deduced by applying
the First Law.
External to the pump, air is always at atmospheric pressure (pa). As air is drawn into the
cylinder, the boundary indicated in the figure below with a dashed line is drawn inwards.
W = -
Piston
Volume Va
Air (ma) drawn
into cylinder.
The work done on the "complete" system, including the air being drawn in, will be:
- [ Padv = -Pa (0-V₁) = Pava
The process is adiabatic, hence Q=0 so that:
W + Q = U₂ - U₁
Applying the first law to the complete system constituted by the cylinder content and air
drawn in, we can write:
Pava = (ma+mp2) cvT4 - mp2CvTc3 - macvTa
But using the perfect gas equation pV=mRT and R+Cv=Cp we obtain:
(ma+mp2) CvT₁ = mp2CvTc3 + map Ta
Transcribed Image Text:Notes: a) b) c) A simplified sketch of the thermodynamic system showing cylinder/piston at initial conditions can be represented as: Gas bottle Valve Cylinder L=0.3m; d = 0.08m Vp/Vc=0.1 and Vb/Vc=0.9 Where V₂= connecting pipe volume, Vc= pump cylinder volume, V₁= bottle volume First cycle of the pump comprises: First compression 1-2: Isentropic compression (valve is open; initial volume being Vc+Vb+Vp) First expansion 2-3: Isentropic expansion. Bottle valve closed Filling of pump and connecting pipe 3-4. Adiabatic Cylinder Orifice To solve point 5 you would need the following result deduced by applying the First Law. External to the pump, air is always at atmospheric pressure (pa). As air is drawn into the cylinder, the boundary indicated in the figure below with a dashed line is drawn inwards. W = - Piston Volume Va Air (ma) drawn into cylinder. The work done on the "complete" system, including the air being drawn in, will be: - [ Padv = -Pa (0-V₁) = Pava The process is adiabatic, hence Q=0 so that: W + Q = U₂ - U₁ Applying the first law to the complete system constituted by the cylinder content and air drawn in, we can write: Pava = (ma+mp2) cvT4 - mp2CvTc3 - macvTa But using the perfect gas equation pV=mRT and R+Cv=Cp we obtain: (ma+mp2) CvT₁ = mp2CvTc3 + map Ta
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