Question

3.32. One mole of an ideal gas, initially at 30°C and 1 bar, is changed to 130°C and 10 bar by three different mechanically reversible processes: The gas is first heated at constant volume until its temperature is 130°C; then it is compressed isothermally until its pressure is 10 bar The gas is first heated at constant pressure until its temperature is 130°C; then it is compressed isothermally to 10 bar The gas is first compressed isothermally to 10 bar; then it is heated at constant pressure to 130°C Calculate Q, W, AU, and AH in each case. Take Cp = (7/2)R and Cy = (5/2)R. Alter- natively, take Cp= (5/2)R_and Cy= (3/2)R.

Answer 1

Solution Answe Tnilia temPe dature and Pdessure of the Sos aje 30 c ond 1 ba Number of moles ot gas is NoU Cadlulate the Volume of the daS USing idCal euoHon HIE-8 X210u mol k 303-S K Now is heatod t constani Nolu me and femn pcatude is incdcoge to o3 Then the go8 iS Compre ssed iSother mallS to Pessude lo ba7 empeatue and PocssuFe ore 403k and 1oba So, Finos

Calulote the Finas Volume uSing ideal gag equolion nR T2 A P2 3_ x403IS K Imole x 8 314 loxios Pa V2 The cP ssion For u) done is g follec^S 2-3 das- 2 V3 RT In - xl¢o 3- 5 K xn -8.31 Mol AU- AU2A2. Tnternal cnengy vdTto -xCloo) Imolex x8 314. 2 2.079 K

EnthalpyA H = AH-2 + A H2.3 nCpdT to x(loo) molk Xdloul 2 2.9 K Heat AU-CWo7k c 2.079 S-674나 PART 2 is 403.1s K and the The temferaiube at stoge -2 Finas Pessuse is lo ba AU2-3 Inteonal enc&gy,Au = AU,2. En(ndTt0 r8 314 \mole x 2 mol le Enthalfs AH -AH-2 A 2.3 ncpdTto x831니 mol 는 - )Mole x : 2.9KJ

At Consta Pdessue POcess DeO-AH AU-AO = 2079 kJ- 2-91k5 O831 K S w3 = nR T, \n mole R8 314 x4o3. 1S xln 83 Kt 3 718 KJ Total ask- 6886 kJ o heat is follocus The ex fdC Ssion Ae : AU - wo K - 6 886ks 2 079KJ PART 3 follos The cbnkone 'in the So theoma Process is g P3 nRT In wi-2

E\Mole * 8 3l4 X 303 15 x In ILad S-803 KJ Intenno요 enengy,au AU2-3 △나-2 C Mole xS x8 3[4 _3 2 x( 10) 기 1ow Enthalfy, AH- ΔW-2 + △H2.3 +hcpd 8.314 xC {99) -2.91KS At constont Pe Ssure PLe SS, AB- AH A 2.3 -2 onk, 23 2.079 KJ- 2.91EJ -o83 KJ 0 831 J +5 GB3 k5 Tota aon- 4.9구2 k3

Tota heat AU-WOd -2.079kJ -4.992 E T Now Peat the CaculaHons Fo Cv R and p 2 te mPenot ue Tniial Prc SSude of the gos op 300 ard and bad Numbe of moles of gos is -the gog uSing idea J Noc CalOlate the Volume if e?uotion \molex8 314 Mo1K No 3ag is heated at Constont volume and demfead ngeged (o Lo3 k. Then the gog is compiessd is iSothenmall to Pessuse So, Final kmPeotuoe «nd Poe ssude ade Lpo3 Kan! loban

he ina Volume using idel S-L eguotion Cal(ulate 2 oxloPa oo335 s The cepession Fa cany done is alfolocus 2 +2.3 w RT n o oO33 Sm x403.1s k xin -3.31L Molk 6.74 K Inlennal enegy,AV-AU2 2 nydTo x(log) nolk 8 314 :IMole x -

EnthaPh AH- AH2 +A112-3 nCpd T+o E1mole x £ xg.3|L J Cay 2.0구9 k3 U -wO&k Heat 12 L7 J -6 74 E J .sIS KS Pante The tem Perature at Sae - 2 i Leo31sk ornd ke Fina Pesu re is lo bod Tntennal en,I9, AU-AU4-2. nCdTo 3 x8 314 (00/ Mol 1.247k5 EnthalpA HE AHi-2 +A2.3 ncpdTt TO x8.314 Mo) \Mo1? x - 2.07 J

At Conslant pre ssure Pecess wooK C! 2 - 247 k-2 079 kJ O 832 S 23nT In P2 J mole ¥ 8 3\ 4 03.15IN ban 772 Total codk 6.886 kJ The epoe sSion fo heat s o follows -AU-Coờ 247と3-6886KI

PA९ त*, ¨Te c.^D «ेo०० `n hc _i So4hen Do9 ?४०(c s:S i S cg-(cts-s g [श) 3 D९ Ta 1n ८०र०. ।० boा - । लo\Q > ४-३\ - X^o३.। ऽ >x\n ) ५४ noK S803 EJ -S8 9n:९.T1 aQ CuC१9». A UU - ८º -9म- L W> -< L P^>u t- ७ F. *71E& x -स X २\°प्य ( Molk (s॰)< - 1 ·२५ १ ४ ऽ + A H* p.. १ \ -2 े E n+ho \?५ ,A H A t ०+n«ृ s T Clos) X 8-९।४ .ऽ - \ तo\& X. त \°L 2 .०+१ r

At constant Pre ssuoa Pdocess Ae- -247 KJ 2.079J -0 831 K T Total co k o83 kJ +5: 803EJ L.92KJ AU - Cwo& k Totul heat -4.972T -3725KS