By Onkar Singh
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Extra resources for Applied Thermodynamics, 3rd Edition
26. A mixture of 18 kg hydrogen, 10 kg nitrogen and 2 kg of carbon dioxide is put into a vessel at atmospheric conditions. Determine the capacity of vessel and the pressure in vessel if it is heated upto twice of initial temperature. Take ambient temperature as 27ºC. Solution: Gas constant for mixture can be obtained as; Rmixture = ( mH 2 . RH 2 + mN2 . 314 kJ/kg . 314 kJ/kg . 314 kJ/kg . 15 kJ/kg . 297 kJ/kg . 189 kJ/kg . 606 kJ/kg . K Considering mixture to be perfect gas; Rmixture = Capacity of vessel Vmixture = Here, mmixture .
A number of mathematical equations of state suggested by Van der-Waals, Berthelot, Dieterici, Redlich-Kwong, Beattie-Bridgeman and Martin-Hou etc. are available for analysing the real gas behaviour. Dalton’s law and Amagat’s law can also be used for real gases with reasonable accuracy in conjunction with modified equations of state. As the ideal gas equation does not conform to the real gas behaviour in certain ranges of pressures and temperatures, so the perfect gas equation should be modified using compressibility factor for the gas at given pressure and temperature.
0 20 _________________________________________________________ Applied Thermodynamics Fig. 13 (c) Generalized compressibility chart, 10 ≤ pR ≤ 40 pressure and reduced temperatures for several gases. On the generalized compressibility chart it could be seen that at “very small pressures the gases behave as an ideal gas irrespective of its temperature” and also at “very high temperatures the gases behave as ideal gas irrespective of its pressure”. 17 VANDER’ WAALS AND OTHER EQUATIONS OF STATE FOR REAL GAS Vander’ Waals suggested the equation of state for real gas in 1873.