ME300HW7Solution

# ME300HW7Solution - SP-18 Methane gas is stored at a...

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SP-18. Methane gas is stored at a pressure of 150 bar and a temperature of -10ºC in a tank with a volume of 10 m 3 . Calculate the mass of methane in the tank using (a) the ideal gas equation of state (b) the generalized compressibility chart (c) the Van der Waals equation of state (iteration required, use ideal gas EOS solution for first guess) (d) EES Solution: (a) Ideal gas EOS 4 4 3 3 8.314 For methane: 16.04 0.5183 16.04 150 100 10 1100 0.5183 10 273.15 CH CH IG kJ kg kJ kmol K M R kg kmol kg K kmol kJ m p m m kg RT kJ K kg K (b) Generalized compressibility chart 4 4 , , 3 3 For methane: 191 46.4 263.15 150 For the tank conditions: 1.38, 3.23 191 46.4 v From the gen comp chart: 0.71 150 100 10 0.71 0.5183 10 C CH C CH R R C C GCC T K p bar T p T p T p p p Z RT mRT kJ m p m m ZRT kJ kg K 1550 273.15 kg K

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(c) Van der Waals EOS 2 6 6 3 2 2 2 3 3 2 3 3 2 2 v v for methane: 2.293 229.3 229.3 0.0428 Table A-24 8.314 263.15 229.3 150 15,000 v v 0.0428 ? 2188 229.3 15,000 v 0.0428 v RT a p b bar m kPa m kJ m a kmol kmol kmol m b kmol kJ kJ m K kmol K kJ kmol p bar m m kmol 3 3 From the ideal gas EOS: 10 16.04 v 0.1458 1100 kg m M m kmol n m kg kmol
Set up an iteration table: v 0.1458 10456 0.1000 15321 0.1100 13610 0.1020 14920 0.1015 15017 0.1016 14997 RHS 3 3 3 From the Van der Waals EOS: v 0.1016 10 16.04 1579 v 0.1016 VDW M m n m kmol kg m M kmol m kg m kmol (d) from EES p_tank = 15000 [kPa] V_tank=10.00 [m^3] T_tank =273.15-10 Ru = 8.314 [kJ/kmol-K] MWCH4= 16.04 [kg/kmol] RCH4=Ru/MWCH4 vCH4=volume(methane,T=T_tank, p=p_tank) massCH4=V_tank/vCH4 Result: From EES: 1572 EES m kg

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SP-19. (a) One (1.0) kg of ammonia (NH 3 ) is contained in a piston cylinder device. The ammonia is present initially as a saturated liquid at a pressure of 2.0 bars and a temperature of -18.86 ºC. Heat is added to the piston cylinder device and the ammonia undergoes a phase change from a saturated liquid to a saturated vapor. The specific volume of the saturated liquid is 3 3 1.507 10 / m kg . Assume that the saturated vapor is an ideal gas. The temperature dependence of the ammonia saturation pressure is given by 2 2 , 67.745 , 0.1502 sat sat sat sat sat dp T T T K p kPa dT kPa kPa where K K
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• Fall '09
• kmol, Tsat

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