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...


3.10 'Compressed air is stored at roo.n temperature (T) and hign pressure<br>(PH) in a rigid tank. A stream of flow rate m is allowed to flow from<br>the tank and is used in order to generate power. The stream is expanded<br>through a turbine, from Py to atmospheric pressure (PL).<br>т, Ри. То<br>m, PL, Tout<br>m, PH To<br>m, PL, To<br>m, PH, To<br>S<br>+ W.<br>To<br>PL. Tout<br>PL, To<br>Figure P3.10<br>PROBLEMS<br>137<br>(a) Assume that the expansion is reversible and adiabatic and report<br>the expression for the specific power output Ws/m as a function of<br>PH/P. Treat the air as an ideal gas.<br>(b) Assume that the expansion occurs reversibly and isothermally<br>(at To) and report the expression for the specific power output<br>Wr/m as a function of P/P.<br>(c) Show that Ws < Wr and explain (in words) why this should be so.<br>(d) After the reversible and adiabatic expansion (a), the air stream is<br>heated from Tu back to To by direct contact with the ambient.<br>See Fig. P3.10 and determine the rate of entropy generation (Sgen)<br>in the control volume indicated with a dashed line. Invoke the<br>Gouy-Stodola theorem to determine the lost power (Wost) that<br>corresponds to Seen- Show that W1ost = WT - Ws, which means that<br>if the expansion is executed reversibly and isothermally (instead<br>of reversibly and adiabatically), then the destruction of power is<br>avoided.<br>

Extracted 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="">

Jun 10, 2022
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