Compressed air is stored at roo.n temperature (T,) and hign 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). m, PH. To + W, m, P, Tout m, P, To - T W m, PL, To m, P. To s > W. To PL, Tout PL. To Figure P3.10 PROBLEMS 137 (a) Assume that the expansion is reversible and adiabatic and report the expression for the specific power output Ws/m as a function of PH/P. Treat the air as an ideal gas. (b) Assume that the expansion occurs reversibly and isothermally (at To) and report the expression for the specific power output WT/m as a function of P/PL. (c) Show that Ws < Wr and explain (in words) why this should be so. (d) After the reversible and adiabatic expansion (a), the air stream is heated from T back to To by direct contact with the ambient. See Fig. P3.10 and determine the rate of entropy generation (Sge in the control volume indicated with a dashed line. Invoke the Gouy-Stodola theorem to determine the lost power (Wost) that corresponds to Sgen- Show that W1ost = WT - Ws, which means that if the expansion is executed reversibly and isothermally (instead of reversibly and adiabatically), then the destruction of power is avoided.
Compressed air is stored at roo.n temperature (T,) and hign 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). m, PH. To + W, m, P, Tout m, P, To - T W m, PL, To m, P. To s > W. To PL, Tout PL. To Figure P3.10 PROBLEMS 137 (a) Assume that the expansion is reversible and adiabatic and report the expression for the specific power output Ws/m as a function of PH/P. Treat the air as an ideal gas. (b) Assume that the expansion occurs reversibly and isothermally (at To) and report the expression for the specific power output WT/m as a function of P/PL. (c) Show that Ws < Wr and explain (in words) why this should be so. (d) After the reversible and adiabatic expansion (a), the air stream is heated from T back to To by direct contact with the ambient. See Fig. P3.10 and determine the rate of entropy generation (Sge in the control volume indicated with a dashed line. Invoke the Gouy-Stodola theorem to determine the lost power (Wost) that corresponds to Sgen- Show that W1ost = WT - Ws, which means that if the expansion is executed reversibly and isothermally (instead of reversibly and adiabatically), then the destruction of power is avoided.
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Transcribed Image Text:3.10 'Compressed air is stored at roo.n temperature (T) and hign 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 Py to atmospheric pressure (PL).
т, Ри. То
m, PL, Tout
m, PH To
m, PL, To
m, PH, To
S
+ W.
To
PL. Tout
PL, To
Figure P3.10
PROBLEMS
137
(a) Assume that the expansion is reversible and adiabatic and report
the expression for the specific power output Ws/m as a function of
PH/P. Treat the air as an ideal gas.
(b) Assume that the expansion occurs reversibly and isothermally
(at To) and report the expression for the specific power output
Wr/m as a function of P/P.
(c) Show that Ws < Wr and explain (in words) why this should be so.
(d) After the reversible and adiabatic expansion (a), the air stream is
heated from Tu back to To 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 (Wost) that
corresponds to Seen- Show that W1ost = WT - Ws, 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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