Lecture 18 - Second law, entropy, examples

Topics For Today * Second Law of thermodynamics * Calculation * Reading : of Entropy Examples Chapter 4 , Suttons 4.1.42 Quick First Law * Review of First ¥0 Internal introduces Law Energy DHEQTW Allows us to perform Energy Balances in dh=dQ+dW * prousus Special case : !2! Mechanically Rev . dW= - PTV Second Law Spontaneous process : aprocessthatonustaredvunsonitsorrnhotSecmdLawWven_XApProachtoequilibrinmisspohtaneous.TwGTf@XHToremoveasyHemfromegnilibnumNemustinterferetromoutside.H0iiijiijiiiiitkiiil.iji.Mathematicalstatementot2ndlawinEntropyCs7NStatefunction02PPiQ.iliiInsiIiIilIiiIkTfotienFFirFnthedirectimofequilibnuminiso1atedsYstem.A A before B after ds At process ds > 0 dS=o dsc 0 : possible process eauilibnium impossible to Relationship :( UN ) fixed Isolated system mS=S( . properties measurable U ,v ) U= UCS ,r or ) dltffddjdstpfut );dv - is First Law ( rev ) debut Conclusion : dU=tQ : T= : To P DV . - rev (0¥ ) calculate 0512 reversible path and dQvev=TdS dS= dated , btw two states , the compute - connect them with a integral #fdQ÷r I Also , a new way to dQvev= calculate Tdsns Qrev in reversible Qreafjtds proud is , cpofsteamisequaltocpis Assume 955=12 ao=4 ( aota.tt#2+93T3+94T4 -395 a ,= - 15,2=5 Setupofsolutim , -101bar , 400°C . . ) 4.186.15392=1.405×105 2 200°C - 93=-1.564.10 8 94=0.632.10 " Tz Exampktcalalatedskforsteamfomlbar p . , =RJ(a¥+a+azT+asTIayT3)dT ,dQ÷u=fCPt÷ z • =Rfao1n¥,+aitzF)+a£( TIF • const .P dQ=CPdT = I 1272111 motk 0.7067 - II Ks .K ) . " } Table E-2: Superheated Steam (part 1 of 5) Temperature (◦ C) P in bar (T sat V 28.186 2419.8 2560.8 8.3939 50 29.782 2444.4 2593.4 8.4976 100 34.419 2516.0 2688.0 8.7700 150 39.043 2588.2 2783.4 9.0097 200 43.663 2661.5 2879.8 9.2251 250 48.281 2736.2 2977.6 9.4216 300 52.898 2812.4 3076.9 9.6027 350 57.515 2890.1 3177.6 9.7713 400 62.131 2969.4 3280.0 9.9293 450 66.747 3050.3 3384.0 10.078 500 71.363 3132.9 3489.7 10.220 550 75.979 3217.3 3597.1 10.354 600 80.594 3303.3 3706.3 10.483 700 89.826 3480.8 3929.9 10.725 0.1 V (45.81) U H S 0.00101 191.80 191.81 0.6492 14.671 2437.2 2583.9 8.1489 14.867 2443.3 2592.0 8.1741 17.197 2515.5 2687.4 8.4488 19.514 2587.9 2783.0 8.689 21.826 2661.3 2879.6 8.905 24.136 2736.1 2977.4 9.101 26.446 2812.3 3076.7 9.283 28.755 2890.0 3177.5 9.451 31.064 2969.3 3279.9 9.609 33.372 3050.2 3384.0 9.758 35.680 3132.9 3489.7 9.900 37.988 3217.2 3597.1 10.034 40.296 3303.3 3706.3 10.163 44.912 3480.8 3929.9 10.405 0.2 V (60.06) U H S 0.00102 251.38 251.40 0.8320 7.648 2456.0 2608.9 7.9072 8.586 2514.5 2686.2 8.1262 9.749 2587.3 2782.3 8.3680 10.907 2661.0 2879.1 8.5842 12.064 2735.8 2977.1 8.7811 13.220 2812.1 3076.5 8.9624 14.375 2889.9 3177.4 9.1311 15.530 2969.2 3279.8 9.2892 16.684 3050.1 3383.8 9.4383 17.839 3132.8 3489.6 9.5797 18.993 3217.1 3597.0 9.7143 20.147 3303.2 3706.2 9.8431 22.455 3480.7 3929.8 10.086 0.5 V (81.32) U H S 0.00103 340.42 340.48 1.0910 3.240 2483.2 2645.2 7.5930 3.4188 2511.5 2682.4 7.6952 3.8899 2585.7 2780.2 7.9412 4.3563 2660.0 2877.8 8.1591 4.8207 2735.1 2976.2 8.3568 5.2841 2811.6 3075.8 8.5386 5.7470 2889.4 3176.8 8.7076 6.2095 2968.8 3279.3 8.8658 6.6718 3049.9 3383.5 9.0150 7.1339 3132.6 3489.2 9.1565 7.5959 3216.9 3596.7 9.2912 8.0578 3303.1 3706.0 9.4200 8.981 3480.6 3929.7 9.6625 1 V (99.61) U H S 0.00104 417.33 417.44 1.3026 1.694 2505.5 2674.9 7.3588 1.6960 2506.2 2675.8 7.3610 1.9367 2582.9 2776.6 7.6147 2.1725 2658.2 2875.5 7.8356 2.4062 2733.9 2974.5 8.0346 2.6389 2810.7 3074.5 8.2171 2.8710 2888.7 3175.8 8.3865 3.1027 2968.3 3278.5 8.5451 3.3342 3049.4 3382.8 8.6945 3.5656 3132.2 3488.7 8.8361 3.7968 3216.6 3596.3 8.9709 4.0279 3302.8 3705.6 9.0998 4.490 3480.4 3929.4 9.3424 1.5 V (111.35) U H S 0.00105 466.92 467.08 1.4335 1.1594 2519.2 2693.1 7.2229 1.2856 2580.1 2772.9 7.4207 1.4445 2656.5 2873.1 7.6447 1.6013 2732.7 2972.9 7.8451 1.7571 2809.7 3073.3 8.0284 1.9123 2888.0 3174.9 8.1983 2.0671 2967.7 3277.8 8.3571 2.2217 3048.9 3382.2 8.5067 2.3762 3131.7 3488.2 8.6484 2.5305 3216.3 3595.8 8.7833 2.6847 3302.5 3705.2 8.9123 2.993 3480.2 3929.1 9.1550 2 V (120.21) U H S 0.00106 504.47 504.68 1.5301 0.8857 2529.1 2706.2 7.1269 0.9599 2577.1 2769.1 7.2809 1.0805 2654.7 2870.8 7.5081 1.1989 2731.5 2971.3 7.7100 1.3162 2808.8 3072.1 7.8940 1.4330 2887.3 3173.9 8.0643 1.5493 2967.1 3277.0 8.2235 1.6655 3048.4 3381.5 8.3733 1.7814 3131.3 3487.6 8.5151 1.8973 3215.9 3595.4 8.6501 2.0130 3302.2 3704.8 8.7792 2.2444 3479.9 3928.8 9.0220 Steam Tables L 0.00101 137.76 137.77 0.4763 Appendix E in C) 0.05 V (32.88) U H S Table E-2: Superheated Steam (part 1 of 5) Temperature (◦ C) P in bar (T sat V 28.186 2419.8 2560.8 8.3939 50 29.782 2444.4 2593.4 8.4976 100 34.419 2516.0 2688.0 8.7700 150 39.043 2588.2 2783.4 9.0097 200 43.663 2661.5 2879.8 9.2251 250 48.281 2736.2 2977.6 9.4216 300 52.898 2812.4 3076.9 9.6027 350 57.515 2890.1 3177.6 9.7713 400 62.131 2969.4 3280.0 9.9293 450 66.747 3050.3 3384.0 10.078 500 71.363 3132.9 3489.7 10.220 550 75.979 3217.3 3597.1 10.354 600 80.594 3303.3 3706.3 10.483 700 89.826 3480.8 3929.9 10.725 0.1 V (45.81) U H S 0.00101 191.80 191.81 0.6492 14.671 2437.2 2583.9 8.1489 14.867 2443.3 2592.0 8.1741 17.197 2515.5 2687.4 8.4488 19.514 2587.9 2783.0 8.689 21.826 2661.3 2879.6 8.905 24.136 2736.1 2977.4 9.101 26.446 2812.3 3076.7 9.283 28.755 2890.0 3177.5 9.451 31.064 2969.3 3279.9 9.609 33.372 3050.2 3384.0 9.758 35.680 3132.9 3489.7 9.900 37.988 3217.2 3597.1 10.034 40.296 3303.3 3706.3 10.163 44.912 3480.8 3929.9 10.405 0.2 V (60.06) U H S 0.00102 251.38 251.40 0.8320 7.648 2456.0 2608.9 7.9072 8.586 2514.5 2686.2 8.1262 9.749 2587.3 2782.3 8.3680 10.907 2661.0 2879.1 8.5842 12.064 2735.8 2977.1 8.7811 13.220 2812.1 3076.5 8.9624 14.375 2889.9 3177.4 9.1311 15.530 2969.2 3279.8 9.2892 16.684 3050.1 3383.8 9.4383 17.839 3132.8 3489.6 9.5797 18.993 3217.1 3597.0 9.7143 20.147 3303.2 3706.2 9.8431 22.455 3480.7 3929.8 10.086 0.5 V (81.32) U H S 0.00103 340.42 340.48 1.0910 3.240 2483.2 2645.2 7.5930 3.4188 2511.5 2682.4 7.6952 3.8899 2585.7 2780.2 7.9412 4.3563 2660.0 2877.8 8.1591 4.8207 2735.1 2976.2 8.3568 5.2841 2811.6 3075.8 8.5386 5.7470 2889.4 3176.8 8.7076 6.2095 2968.8 3279.3 8.8658 6.6718 3049.9 3383.5 9.0150 7.1339 3132.6 3489.2 9.1565 7.5959 3216.9 3596.7 9.2912 8.0578 3303.1 3706.0 9.4200 8.981 3480.6 3929.7 9.6625 1 V (99.61) U H S 0.00104 417.33 417.44 1.3026 1.694 2505.5 2674.9 7.3588 1.6960 2506.2 2675.8 7.3610 1.9367 2582.9 2776.6 7.6147 2.1725 2658.2 2875.5 7.8356 2.4062 2733.9 2974.5 8.0346 2.6389 2810.7 3074.5 8.2171 2.8710 2888.7 3175.8 8.3865 3.1027 2968.3 3278.5 8.5451 3.3342 3049.4 3382.8 8.6945 3.5656 3132.2 3488.7 8.8361 3.7968 3216.6 3596.3 8.9709 4.0279 3302.8 3705.6 9.0998 4.490 3480.4 3929.4 9.3424 1.5 V (111.35) U H S 0.00105 466.92 467.08 1.4335 1.1594 2519.2 2693.1 7.2229 1.2856 2580.1 2772.9 7.4207 1.4445 2656.5 2873.1 7.6447 1.6013 2732.7 2972.9 7.8451 1.7571 2809.7 3073.3 8.0284 1.9123 2888.0 3174.9 8.1983 2.0671 2967.7 3277.8 8.3571 2.2217 3048.9 3382.2 8.5067 2.3762 3131.7 3488.2 8.6484 2.5305 3216.3 3595.8 8.7833 2.6847 3302.5 3705.2 8.9123 2.993 3480.2 3929.1 9.1550 2 V (120.21) U H S 0.00106 504.47 504.68 1.5301 0.8857 2529.1 2706.2 7.1269 0.9599 2577.1 2769.1 7.2809 1.0805 2654.7 2870.8 7.5081 1.1989 2731.5 2971.3 7.7100 1.3162 2808.8 3072.1 7.8940 1.4330 2887.3 3173.9 8.0643 1.5493 2967.1 3277.0 8.2235 1.6655 3048.4 3381.5 8.3733 1.7814 3131.3 3487.6 8.5151 1.8973 3215.9 3595.4 8.6501 2.0130 3302.2 3704.8 8.7792 2.2444 3479.9 3928.8 9.0220 ¥ : ⇐ 5451 - 7.8356070951¥ 8k Steam Tables L 0.00101 137.76 137.77 0.4763 Appendix E in C) 0.05 V (32.88) U H S EXAMPLE 2 : Calculate the entropy of Method I @ 1bar Water , Sotwm pressed From steam tables : S 20°C . liquid '@zooc= a Sot sat . L@ same 0.2695 20°C ' •S= 0.2965 Method I calculate from sat . L @ 1bar kJ1kg.K1baroYHHE6_ms@C1bar.2ooHr-O.296SkJ1ks.K 3 Sz+§p' 52=1.3026 ¥ Sz=sz+Jt¥= 2 Cpt 4.18 KJHGK KJIKO Tz= Sz = 02984 k5/Kg K . . Tz=Z 372.76k K 93.15k = 52+9>1 NIH 't . EXAMPLE 3 Calculate : with Solution : S= @ lever Xe 20bar , . Rule Set the 30% entropy of wet steam moisture @ 20bar : xvsv 212.38°C : 2,4470 KJIKOK S✓= 6.339214119 K XL 0.3 SL= = Xv= . 0-7 X S = 5.17154 kJ/1g . K EXAMPLE 4 Solution P : Calculate Dsrapofhexaneae Additional data # 10bar . dsrap¥dQ@=÷m{dQ=#ITa . .tt#@10bar=165.09,6AHrap=20.675kJ/mo1 ✓ = 20.625=0.04717 438.24k kJ/mo1 . K Summary is + Entropy * General Recipe a thermodynamic properly new ** Bsn : Special Case : for anti compressed big satlig @ same , -1M¥ .P dQ=tH : DS *s¥ b k' ¥ - approximately equal ÷ to temperature lever Rule applies The definition of entropy exactly how to is calculate very intuitive mol it . . Even so , we know