標題:
熱力學問題van der waal eq.
發問:
one hundred moles of hydrogen gas at 298k are reversibly and compressed from 20 to10 liters. The van der waals constants are a=0.2461 , b=0.02668 ,and in the range of pressure 1~1500 atm . the virial equation for hydrogen is PV=RT(1+6.4*10^-4P) . Calculate the work that must be done on the system to effect the... 顯示更多 one hundred moles of hydrogen gas at 298k are reversibly and compressed from 20 to10 liters. The van der waals constants are a=0.2461 , b=0.02668 ,and in the range of pressure 1~1500 atm . the virial equation for hydrogen is PV=RT(1+6.4*10^-4P) . Calculate the work that must be done on the system to effect the required change in volume and compare this with the values that would be calculated assuming that (a) hydrogen behaves as a van der waal gas and (b) hydrogen behaves as an ideal gas.
最佳解答:
為計算方便起見，將氣體體積改為以莫耳體積為變數。故題目改為從0.2 L/mol壓縮至0.1 L/mol。 Virial Equation of State: PV / RT = 1 + BP; B = 6.4 x 10^-4 ＝＞P = RT / (V - BRT)..........................(1) van der Waal Equation of State: (P + a / V^2) x (V - b) = RT ＝＞P = RT / (V - b) - a / V^2.....(2) Ideal gas Equation of State: PV = RT＝＞P = RT / V.......(3) 上述各式中所有的V皆為莫耳體積。 W = 100mol x 積分(0.2到0.1)PdV 由式(1), W = 100 x 0.082 x 298 x ln[(0.1 - 6.4 x 10^-4 x 0.082 x 298) / (0.2 - 6.4 x 10^-4 x 0.082 x 298)] = -1910.384 atm.L = -193570 Joule 由式(2), W = 100 x { 0.082 x 298 x ln[(0.1 - 0.02668) / (0.2 - 0.02668)] + 0.2461 x (1 / 0.1 - 1 / 0.2)} = -1979.194 atm.L = -200542 Joule 由式(3), W = 100 x 0.082 x 298 x ln(0.1 / 0.2) = -1693.774 atm.L = -171622 Joule 負號表外界對系統作功。
此文章來自奇摩知識+如有不便請留言告知
其他解答:
到下面的網址看看吧 ??http://*****FBEFE3C2E0474026
留言列表
