安工大物理化学C1练习
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考试时间:2012-7-8, 9:00-11:00,东教D305 1 2-5 始态为25℃,200kPa的5 mol 某理想气体,经a,b两不同途径到达相同的末态。途径a先经绝热膨胀到 – 28.57℃,100kPa,步骤的功Wa= - 5.57kJ;在恒容加热到压力200 kPa的末态,步骤的热Qa= 25.42kJ。途径b为恒压加热过程。求途径b的Wb及Qb。 解:过程为:
200,42.25200,57.510200510057.285200255VkPaCtmolVkPaCmolVkPaCmolaaaaWkJQQkJW
途径b 33111062.0)10200(15.2983145.85/mpnRTV
33222102.0)10100()15.27357.28(3145.85/mpnRTV
kJJVVpWambb0.88000)062.0102.0(10200)(312 kJWWWaaa57.5057.5 kJQQQaaa42.2542.250
因两条途径的始末态相同,故有△Ua=△Ub,则 bbaaWQWQ kJWWQQbaab85.270.857.542.25 2-7 已知水在25℃的密度ρ=997.04 kg·m-3。求1 mol 水(H2O,l)在25℃下: (1)压力从100 kPa 增加到200kPa 时的△H;(2)压力从100 kPa 增加到1 MPa 时的△H。 假设水的密度不随压力改变,在此压力范围内水的摩尔热力学能近似认为与压力无关。 解:)(pVUH 因假设水的密度不随压力改变,即V恒定,又因在此压力范围内水的摩尔热力学能近似认为与压力无关,故0U,上式变成为
)()(12122ppMppVpVHOH
(1)JppMHOH8.110)100200(04.9971018)(33122
(2)JppMHOH2.1610)1001000(04.9971018)(33122* 3-12 2 mol双原子理想气体从始态300K,50 dm3 ,先恒容加热至 400 K,再恒压加热至体积增大至 100m3,求整个过程的Q,W,△U,△H及△S。 解:过程为
032030131,100 2,50400 2,50300 2pdmTmolpdmKTmolpdm
KTmol?双原子气体双原子气体双原子气体恒压加热恒容加热
PaPaVRTp99774)}1050/(3003145.82{/2311 PaPaTTpp133032}300/40099774{/1010
KKnRVpT05.800)}3145.82/(10100133032{)/(31202 W1=0; W2= -pamb(V2-V0)= {-133032×(100-50)×10-3} J= - 6651.6 J 考试时间:2012-7-8, 9:00-11:00,东教D305 2 所以,W = W2 = - 6.652 kJ
kJJJRTTnCHmp10.2929104)}30005.800(272{)(12,
kJJJRTTnCUmV79.2020788)}30005.800(252{)(12, Q = △U – W = (27.79 + 6.65)kJ≈ 27.44 kJ
02,10,lnlnTTnCTTnCSSSmpmVpV
= {40005.800ln272300400ln252RR} J·K-1 = 52.30 J·K-1 3-13 4 mol 单原子理想气体从始态750 K,150 kPa,先恒容冷却使压力降至 50 kPa,再恒温可逆压缩至 100 kPa。求整个过程的Q,W,△U,△H,△S。 解:过程为
kPaVTTmolkPapVTmolkPapVKTmol100, 450, 4150,750 4202010111单原子气体?单原子气体单原子气体可逆压缩恒容冷却
KKppTT250}150/75050{/1010 01W, kJJJppnRTWW763.55763)}50/100ln(2503145.84{)/ln(0202 02U,kJJJRUU944.2424944)}750250(234{1
02H,kJJJRHH57.4141570)}750250(254{1 Q = △U – W = (-24.944 – 5.763)kJ = - 30.707 kJ ≈ 30.71 kJ
0210,lnlnppnRTTnCSSSmVTV
= {50100ln4750250ln234RR} J·K-1 = - 77.86 J·K-1 3-14 3 mol 双原子理想气体从始态100 kPa ,75 dm3,先恒温可逆压缩使体积缩小至 50 dm3,再恒压加热至100 dm3。求整个过程的Q,W,△U,△H,△S。 解:过程为
2023201301131
,100 3,50 3100,75 3ppTdmVmolpTdmVmolkPapTdmVmol双原子气体?
双原子气体双原子气体恒压加热恒温可逆压缩
KKnRVpT68.300)}3145.83/(107510100{)/(33111 kPaPaKVnRTp150150000)}1050/(68.3003145.83{/3010 KKnRVpT36.601)}3145.83/(1010010150{)/(33222 )()/ln(02010121VVpVVnRTWWW J}10)50100(10150)75/50ln(68.3003145.83{33 = - 4459 J = - 4.46 kJ
01U,kJJJRUU75.1818750)}68.30036.601(253{2
01H,kJJJRHH25.2626250)}68.30036.601(273{2 Q = △U – W = (18.75 + 4.46 )kJ = 23.21 kJ 考试时间:2012-7-8, 9:00-11:00,东教D305 3 02,10,lnlnTTnCppnRSSSmpprT
= {68.30036.601ln273100150ln3RR} J·K-1 = 50.40 J·K-1 3-15 5 mol 单原子理想气体从始态 300 K,50kPa,先绝热可逆压缩至 100 kPa,再恒压冷却使体积缩小至 85 dm3,求整个过程的Q,W,△U,△H,△S。 解:过程示意如下:
22320001
11,,85 5100, , 5 50,300, 5pTdmVmolkPapTVmolkPapKTVmol
单原子气体?单原子气体?
单原子气体恒压冷却热绝热可逆压缩
KKTppTmpCR85.395}300)50/100{()/(5/21/100, 33300016456.0)}10100/(85.3953145.85{/mmpnRTV
01Q,kJJJRUW977.55977)}30085.395(235{11 KKnRVpT47.204}314.85085.0100000{222 W2 = - pamb ( V2 – V1 ) = {- 100×103×(85 – 164.56)×10-3} J = 7956 J W = W1 + W2 = 13933 J = 13.933 kJ
JJRU11934)}85.39547.204(235{2 △U = △U1 + △U2 = -5957 J = - 5.957 kJ kJJJRH930.99929)}30047.204(255{ kJkJWUQQ89.19)956.7934.11(22 1102,66.68}85.39547.204ln255{ )/ln(0KJKJRTTnCSSS
mpPr绝热,
3-16 始态 300 K,1Mpa 的单原子理想气体 2 mol,反抗 0.2 Mpa的恒定外压绝热不可逆膨胀平衡态。求整个过程的W,△U,△H,△S。 解:Q = 0,W = △U
)(23)(23)(121121212TTRnpnRTpnETpTTRnVVpambambamb
代入数据整理得 5T2 = 3.4 T1 = 3.4×300K;故 T2 = 204 K kJJJRUW395.22395)}300204(232{2kJJJRH991.33991)}300204(252{
11111212,73.10729.10}762.26033.16{ }12.0ln2300204ln252{ lnlnKJKJKJKJRR
ppnRTTnCSmp
3-23 甲醇(CH3OH)在101.325kPa 下的沸点(正常沸点)为64.65℃,在此条件下的摩尔蒸发焓△vapHm = 35.32 kJ·mol-1。求在上述温度、压力条件下,1 kg液态甲醇全部变成甲醇蒸气时的Q,W,△U,△H及△S。