Adiabatic Expansion Or Compression Of Air
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Adiabatic Expansion Or Compression Of Air

Air is a mixture of gases constituted mostly by nitrogen and oxygen. Often it is necessary to expand or compress air. Isothermal expansion or compression; and adiabatic expansion and compression are frequently encountered.
(a) When is an expansion or compression Isothermal?
(b) When is an expansion or compression adiabatic?
(c) 165 cubic feet of air at a pressure of 15 psi (pounds per sq in) is compressed adiabatically to a pressure of 80 psi. What is the new volume of the air?
(d) Suppose the volume of air in (c) is compressed isothermally. What will be the volume of air after compression?

The strings:
The string can be grouped as a force problem or a volume problem.
It is grouped as a volume problem since we are calculating compressed volume : S7P1A15 (containership-volume).

The math:
Pj Problem of Interest is of type force (force-push).

(a) An expansion or compression of air at constant temperature is isothermal

(b) An expansion or compression of air without transmission of heat to or from it, is adiabatic

(c) Formula of interest:
V2 = V1(P1/P2)γ. Where:
V1 = volume before compression
P1 = pressure of V1
V2 = volume after compression
P2 = pressure of V2
γ = adiabatic index = Cp/Cv
Cp = heat capacity of air at constant pressure
Cv = heat capacity of air at constant volume

So, V2 = 165(15/80)0.71 = 50 cubic ft.

(d) There is no adiabatic index for isothermal compression
So, V2 = 165(15/80) = 31 cubic ft.

Math

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