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ID: 1868073 • Letter: I

Question

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HOW DO WE KNOW Q IS NEGATIVE? ISNT THE TEMPERATURE INCREASING?

Air is compressed at steady state from 1 bar, 300 K, to 6 bar with a mass flow rate of 4 kg/s. Each unit of mass passing from inlet to exit undergoes a process described by pv1.27 = constant. Heat transfer occurs at a rate of 46.95 kJ per kg of air flowing to cooling water circulating in a water jacket enclosing the compressor. If kinetic and potential energy changes of the air from inlet to exit are negligible, calculate the compressor power, in kW.

HOW DO WE KNOW Q IS NEGATIVE? ISNT THE TEMPERATURE INCREASING?

KNOWN: Air is compressed at steady stute from a given initial state to a given flùal pressure. The mass flow is known, and each unit ·f mass undevsoes pecified process in going from inlet to exit EINp Determine the compressor power 2 T. l.27 ar compressor bar 3oo K ENGE MODELThe conhrol volume is at stead stole. (2) Eaclu uuit of ? mass undergoes a process described by V.474xstaut. (a) The ar an oe modeledas a? ideed gas.(4) kinetic and potential energy effects are nejligible ANALYSIS: To determine the power, begiu witk mass and energy rate bulans af steady state where ni, m. a n and the ndicated terms ave delefed by assum fiön 4. Rearramgiy avvangivg end solving for W LV CV ow, specMieetlpy h, is read from Table A-22 at Sook: he300.1 To get T, ,we use ??. 3.56 with n , 27 (3ook439.1 k Interpolating ?n Table A-22; h,-4 40 .? kT/kg. Inse 'ng values in (+) I kW -750 kw I. The applicability of the ideal gas model can be checked by raference to the genevalizeel compressibilitj chart control volume, as expecfed negative Sign for power de notes eergy +ansfer b? work ute the t

Explanation / Answer

Here control volume is defined as air compressor boundary. During the compression process the temperature of air will rise, to reduce the increased temperature, we extract heat from the compressor by means of cooling water as described in in question details, so here heat is being extracted from the control volume(system).

Now it is the standard notion when the HEAT is provided to the system( control volume) it is considered as positive and when heat is extracted or system(control volume) rejects heat, it is considered as negative, here heat is extracted from system hence heat is written with negativel sign. It is just opposite for work, so when system provide work it is positive and when work is done on the system, then work is negative.