MEEN 315, SECTION 503 PRINCIPLES OF THERMODYNAMICS Spring 2013 Homework #5 DUE February 19, 2013 N.B. The material on this homework is covered on your Exam #1. Exam #1 is Thursday, February 21 from 7 – 9pm in 102 Zachary. This homework will not be graded before the exam. Thus, make a photocopy of it before submission if you wish to use it as a study guide. N.B. The online enhancement lecture “Example: SS Polytropic Process” may be helpful for this assignment. You can access it on elearning, under the Lectures --> Enhancement Lectures --> Example SS Polytropic Process folder. 1. Show the following processes on T-s and P-v diagrams: a) Water initially at T = 50C, P = 5MPa to T = 400C at constant pressure. b) R-134a initially at P = 5 psia, saturated vapor to P = 100 psia at constant entropy. c) Air initially at T = 700K, P = 500 kPa to T = 2000K at constant volume. 2) By evaluating reduced temperatures and pressures, make an assessment if the following can be modeled as an ideal gas. a) Water at T = 200F, P = 14.7 psia b) Air at T = 300K, P = 100kPa (“room temperature” air) c) Methane (CH4) at T = 80F, P = 14.7 psia (roughly natural gas at room temperature air) 3) Internal combustion engines, which use pistons and cylinders to form thermodynamic systems (e.g., the “combustion chamber”), have a process (i.e., the compression process) that compresses air from a low pressure to a high pressure. This happens before combustion begins. This process is ideally modeled as being “isentropic”, which means entropy stays constant during the process (like 1b above). Isentropic process is one of the more important processes we will study this semester; it happens in more than just internal combustion engines or piston/cylinder systems. Suppose air is compressed isentropically (entropy stays constant) from an initial pressure of 14.7 psia and an initial temperature of 300 K to a final pressure of 270 psia. What is the final temperature, the change internal energy, and the change in enthalpy of the ideal gas? 4) Consider a pump which increases the pressure of water from 70 kPa at the inlet to 700 kPa at the outlet. The water enters the pumps at 15C through a 1-cm diameter opening and exits through a 1.5-cm diameter exit. The mass flow rate of water through the pump is 0.5 kg/s. a) For the given conditions, determine the velocity of the water at the inlet and the exit of the pump. b) Suppose instead the water is at 40C (instead of 15C); will the velocities change substantially? What if the water were at 150 C? 5) Air enters a compressor operating at steady state with a pressure of 14.7 psia, a temperature of 70 F, and volumetric flow rate of 500 ft3/min. The air velocity in the exit pipe is 700 ft/s and the exit pressure is 120 psia. If each unit mass of air passing from inlet to exit undergoes a process described by Pv1.34 = constant, determine the exit temperature in F, and the diameter of the exit pipe in inches.Show the following processes on T -5 and P-v diagrams: a) Water initially at T = 50C, P = 5MPa to T = 400C at constant pressure. b) R-l34a initially at P = 5 psia, saturated vapor to P = 100 psi a at constant entropy. c) Air initially at T = 700K, P = 500 kPa to T = 2000K at constant volume. 0.) W,,4e. -p; S-MPQ..) 't= SOc.. } I 7;. " 'i00 c.. J 'PQ := S-M PI>t (C-.nIJU flVl>vWl f~s) II"" 'T ------? v ~ "~rs.7"'-p~ =-(0() jS'-"LT, ..-+00 K: P, "soo k?, 1:1. = ;)000 K ( c.c,'lS 1-+ Va 4J*1e POI '" P. T:1. T, itT"~"'::.;-(O.~IW ~<~~(~) ".. O.+S ~-K -"') ® ~ Y.10 ("",,,);)coo ~ ,®\ 1« Oil., 11-oo+1-_i 10_____-1____L I t-I s ~b,S= o. +s --""'> S:t .s , ..lSL... ~-;:;By evaluating reduced temperatures and pressures, make an assessment if the following can be modeled as an ideal gas. a) Water atT = 200F, P = 14.7 psia b) Air at T 300K. P = IOOkPa ("room temperature" air) c) Methane (CH4) at T = 80F, P = 14.7 psia (roughly natural gas at room temperature air) ~) W ...il!f ... t T: ;)00 FJ p; 1'1.1-r":"'" -Ai p::: 14. '7 f"":"'/ T~"'-t-.,. :J I;) F ~ To(. ~".. .. P.7llf. ';*-(>';I~. T +Iut ~ <) /.u';""a (/o.YIttot /,C-~WI"5 (/1\ l~tJr-b) A,', tl-I:-T", ?oD ~I ',7 lOt) k f:>c.<.. Thll t'~ CI~tk{,.<. 0<..1(-/ ~I:!. 't'SIU)V~. '7 c1wJ-Ckl5 ? 6 j 4,e;.tl/ ::: ) 3 .;1• .s;-K (J 4.1\' P...:t.t..f, = '5. ~+ I'1p" I#\.~r 804. c.erJ.i<ms.1/1e.~..i7 " !/o.t. i -Ite:<P10,,/f'j P~t, i .•;.J) 3r?o ~[::rJJ G«s J 'f'~ e.."..J "~"c:<t t.'io,{,.8. ~l T~(1.r &."" 1Internal combustion engines, which use pistons and cylinders to form thermodynamic systems (e.g., the "combustion chamber"), have a process (i.e., the compression process) that compresses air from a low pressure to a high pressure. This happens before combustion begins, This process is ideally modeled as being "isentropic", which means entropy stays eonstant during the proeess (like lb above). Isentropic process is one of the more important processes we will study this semester; it happens in more than just internal combustion engines or piston/cylinder systems, Suppose air is compressed iscntropically (entropy stays constant) from an initial pressure of 14,7 psia and an initial temperature of 300 K to a final pressure of 270 psia, What is the final temperature, the change internal energy, and the change in enthalpy of the ideal gas? (,tkJrJ P,~ t'l.f. r"<o.. Po. = nc>rs.L~ T, :: 30D 1<..:: (10 F' f~+,\c; (W\+rcr5 ~~s:::':~l) b..~ ~ R....,.. ;; O. C:>(Q S' st;;;: A-\ E. oc -r;,.6l.t A-c;l E) A-gE)~...~ ::' O. J'-\D0.1 -'\ ~ ~u. = c.. ..r .t:.T Co-J"" : ( =-..,-I b..-~ r---='-':;":'(0:...:.,_I+:...I~I't'!.:J-fl.!li.-J-~1 J 9:.. -5.& 0 ) r-::.U:; I;J 'f - I !fI:!Consider a pump which increases the pressure of water from 70 kPa at the inlet to 700 kPa at the outlet. The water enters the pumps at 15C through a I-em diameter opening and exits through a 1.5-cm diameter exit The mass flow rate of water through the pump is O,S kg/so a) For the given conditions, determine the velocity of the water at the inlet and the exit of the pump. b) Suppose instead the water is at 40C (instead of ISC); will the velocities change substantially? What if the water were al 150 C? S<,) bl~Ce..-Wc....J.e... ~.Jv..k ( ; $.J.c...k .;;(. P,.: 70 kP",-p.. ~ +-oO'f::"~ T".:-'5', C. T~ :: .7 cAl :;:" I -c:..""" J 2 " J. SO-<:,,,,,, -rI'"t>c.~ s!,. : Pv"'l; VIA CJ.~ ""-1/.s.-'" .--" <t) f'~cI Vi ~ \,.( -Ii ..J:•!.v\= A V.: ::; Ac \..{ y.0