Thermodynamics

E in E out ¢E systemChapter 2 | 75⎫ ⎪⎬⎪⎭⎫⎪⎬⎪⎭Net energy transferby heat, work, and massChange in internal, kinetic,potential, etc., energiesW sh,in Q out ¢U U 2 U 1100 kJ 500 kJ U 2 800 kJU 2 400 kJTherefore, the final internal energy of the system is 400 kJ.EXAMPLE 2–11Acceleration of Air by a FanA fan that consumes 20 W of electric power when operating is claimed todischarge air from a ventilated room at a rate of 0.25 kg/s at a dischargevelocity of 8 m/s (Fig. 2–48). Determine if this claim is reasonable.Solution A fan is claimed to increase the velocity of air to a specified valuewhile consuming electric power at a specified rate. The validity of this claimis to be investigated.Assumptions The ventilating room is relatively calm, and air velocity in it isnegligible.Analysis First, let’s examine the energy conversions involved: The motor ofthe fan converts part of the electrical power it consumes to mechanical(shaft) power, which is used to rotate the fan blades in air. The blades areshaped such that they impart a large fraction of the mechanical power of theshaft to air by mobilizing it. In the limiting ideal case of no losses (no conversionof electrical and mechanical energy to thermal energy) in steadyoperation, the electric power input will be equal to the rate of increase of thekinetic energy of air. Therefore, for a control volume that encloses the fanmotorunit, the energy balance can be written asE # in E # out⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭⎫⎪⎪⎬⎪⎪⎭Rate of net energy transferby heat, work, and mass dE system > dt→0 1steady2Rate of change in internal, kinetic,potential, etc., energies 0S E # in E # outAir8 m/s FanFIGURE 2–48Schematic for Example 2–11.© Vol. 0557/PhotoDiscSolving for V out and substituting gives the maximum air outlet velocity to beV out BW # elect,in2m # airW # elect, in m # air ke out m # air V2 out220 J>s B 2 10.25 kg>s2a 1 m2 >s 2b 6.3 m>s1 J>kgwhich is less than 8 m/s. Therefore, the claim is false.Discussion The conservation of energy principle requires the energy to bepreserved as it is converted from one form to another, and it does not allowany energy to be created or destroyed during a process. From the first lawpoint of view, there is nothing wrong with the conversion of the entire electricalenergy into kinetic energy. Therefore, the first law has no objection to airvelocity reaching 6.3 m/s—but this is the upper limit. Any claim of highervelocity is in violation of the first law, and thus impossible. In reality, the airvelocity will be considerably lower than 6.3 m/s because of the losses associatedwith the conversion of electrical energy to mechanical shaft energy, andthe conversion of mechanical shaft energy to kinetic energy or air.