Compressed air is stored at room temperature (T 0 ) and high pressure (P H ) in a rigid tank. A…

Compressed air is stored at room temperature (T0)
and high pressure (PH) in a rigid tank. A stream of flow rate
m_ is allowed to flow from the tank and is used in order to generate
power. The stream is expanded through a turbine, from PH to
atmospheric pressure (PL).

(a) Assume that the expansion is reversible and adiabatic
and report the expression for the specific power output __S___
as a function of PH_PL. Treat the air as an ideal
gas.

(b) Assume that the expansion occurs reversibly and
isothermally (at T0) and report the expression for the specific
power output __T ___ as a
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Compressed air is stored at room temperature (T0)
and high pressure (PH) in a rigid tank. A stream of flow rate
__ is allowed to flow from the tank and is used in order to generate
power. The stream is expanded through a turbine, from PH to
atmospheric pressure (PL).

(a) Assume that the expansion is reversible and adiabatic
and report the expression for the specific power output __S___
as a function of PH_PL. Treat the air as an ideal
gas.

(b) Assume that the expansion occurs reversibly and
isothermally (at T0) and report the expression for the specific
power output W_T ___ as a function of PH/PL.

(c) Show that __S <>T
and explain (in words) why this should be so.

(d) After the reversible and adiabatic expansion (a), the
air stream is heated from Tout back to T0 by direct
contact with the ambient. See Fig. P3.10 and determine the rate of entropy
generation (Sgen) in the control volume indicated with a dashed
line. Invoke the Gouy–Stodola theorem to determine the lost power (__ lost)
that corresponds to Sgen. Show that __ lost =
__T _ __ S, which means that if the
expansion is executed reversibly and isothermally (instead of reversibly and
adiabatically), then the destruction of power is avoided.

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