Thermodynamics in Chemical Engineering: Midterm Exam Solutions, Exams of Engineering Chemistry

Download Thermodynamics in Chemical Engineering: Midterm Exam Solutions and more Exams Engineering Chemistry in PDF only on Docsity! Name: 6Sl Discussion section' Su luh'o^SID: Chemical Engineering Thermodynamics 141- Spring 20Ll Tuesday, February 22, zOLl Midterm | - 70 minutes - 100 total points One one-sided 8.5"x 11" equation sheet allowed (20 points) L. Consider an ideal gas. i) (2 points) On the P-V diagram shown below, draw an isothermal curve at T1. ii) (3 points) Show graphically the reversible work for compression from 2Vr to Vr at constant temperature T1. P\ T, i i i ) (6 points) Show mathematical ly that the reversible work done on the system at Tr is greater than at T2 where Tr > Tz. Begin from the definition of work' [\M= _ ?JV Q-1 tW= \Jv =) w= [4",v,V r y S,n( e VJ is A conslant, wi.- c?Q fi"h ib oul o.l t 1," ,r l-egr"l . M" k Lhrl Ne orye tfu?t,rl,r 'S &o-u,LV,U b" V; ,u, W = Rtl+ =) W= - fu l-+, ZV, W,= Vl,/,nz W,. = KT;l^z T, )a, -) W, t \fu, I iv) (3 points) Which one of the following expressions does not remain constant in the reversible and adiabatic expansion of an ideal gas? a) Tvn/cu b) TVl:1 @ r* d ) P V l R/cn C2ED v) (6 points) Prove that all the o_tfer expressions remain ..ttl1[ Begin from the 1't Law. /u =7disw j" =o,adia,r du=5ru i'it'Ju:tnS1 c )T= - wlv -)-v I t- q_ lV =>Cvd t= - v Cv dT Jv - = l<-T v C, l^T r !^V t c=) f q/a = v exyG\ =' l vF/cv =(*p|* ,) Kfc, P ED K C, To" So i) ral l= :Q-l = cv) tr-ll^'' lv K/c vv R.-) =- ) r K Y-l V' = c, ?V, : C,P OED (40 points) 3. A 2 kg copper block is taken out of a furnace at 250'C and quenched in a 10 L oil bath at an initial temperature of 40"C. The specific heat (Cp = Cv) for oil and copper are 7.7 kJ kg-l K'l and 0.39 ru kg-l 6-r respectively. The density of oil is 0.9 g/cm3. i) (5 points) What is the final temperature of the system? l],a ,,1 I a sgsk^ is isuloLa'l ot^ J h,: {,no,,l lorn)^rt. So [A=o a^A 6tnl=-(), S" r r l lLa 0 Jurb, = e :) JUr,+) uu;r = o. 01sT - 115= 6lz - 15 b-T AUr,= -AU'il '-) ff ic,C,^AL =-YYloilCri tAT,il 051 ot/br(l-zso) - ? tfl.)7 tqhKUto-T ) ii) (5 points) How much heat does the copper transfer to the bath? lf wa Cons))er Ll',e otL L-Lh dU-wyf' r)rt coil dT = F0- --) (to z -Lt D) a$ ou r SysL-n = 1kA t 7a\lUKA = hcoit AT 156 06 I i i i ) ( ls points) AScu : = fia C.n where B dU = 8a rSN )U=Sa.*) = 5 J K - 1 s - 1 . W e- , 6.SSil rnL so StU = e. What is the change in entropy of the copper block, oil bath, and universe (in = o,S7s kT/f (' 'r ' -frn Lhn- oil A S", - tEQ'- : I JU ^'l-ttar J,rii-rd; tt: ;Y' = lr-- J r AS";l r I : = ylt"i lCoit lrE- = | i.tx/1,,r.7 ;,1$tu?tr T,o,t T s=,n',r^' -,', T :J':'!kThffi - n r)qn r,T /1,, o-i3^,,t9^ tbt6, is,isolokd, Lh,.= 0,4to h_Tl14 *Mp;j e^;q_ ,f JU"r,i)l:J';A,o ,s >;:" 'o ' v ' - 5o A / 70/ /\Srni v=AS. +AS ,r^.(L1 , -r -r,t ,ff\srr. - 0, trS lSflt>o 'T t . ^ t I r '0 ' n )) rnLa n> 'l ha- fyoLess , s I rre re rs) ble . iv) (15 points) How long does it take to cool the oil bath back to 40"C if the ambient temperature, To, is equal to 20'C? The oil loses heat at a rate of: Q=U'A(T -7" )= B(T -7 , ) JT ff-r,) - YQotl W,l"il Jt LO r l l r I d L r - ro ) i r - r \/ I l - l o ) ?02 \ / twloi l Coi l t/1 o &ronff* i^ uul ,^4, coil ol-f co;toft = b(T -7"\ Jt =) 5-Es-l lynoo.JY)lf z \ L =-306o I Lp' ' f tr 3 )26 l s 'J 21"' ' i^ The thermal expansion coefficient, o,, and the isothermal compressibility, r, of a gas are given by the following expressions: o =!({'l = r, c, 7t',-',)'', v\ar )P 'cv -t( av\ k" i r - = - t - t - - v\aP)r P where k1 and k2 ar€ constants. Cp and Cv may assumed to be independent of temperature. i) (14 points) Derive a volume explicit equation of state, i.e. V = (T,P). I t?V \ t Cr- TUr-c,)/6*=T w )r- k' ', f a!-.t - t +- v l Gr-(,)f r, =fo /cn'( lflr3ktcy' t # = I, [ -rY;'T :) ( 'lV = k, Iff Y-tdT :) J V I J" !^V = k, -fr + c (il (') ,since- ulL [re,[ur^") lL-) - c^lr^ lrfiun\ @ .o ntl, n)- v laPlr P dv -- +.4 -> 1 -zr lrv = L,l'nP +cfi) 0\ 0) anot b\ ) | v= exp (k,-tt) P-^'L - I I ,ro points) 4. I l L I - l-/ K (o^tJ "f^6 =;) l^V