The relationship between pressure (in kPa), temperature(inKelvin), and the specific volume (in- m³/kg) ofa-gas can-be expressed by the-Redlich-Kwong-equation of state as-follows:¶ RT p = v – b a v(v+ b)VT 0.427R²T?* /Pc; dan-b = Where R=universal gas constant (0.518 kJ/kg.K), a = 0.0866R T./ Pe: where T, and p, are critical temperature and the critical pressure ofthe gas," respectively. The transportation of compressed natural-gas (CNG) uses a special tank that can withstand-high- pressure and-lowtemperature. Assume that the CNG-contains 100% methane (critical- temperature =191-K, critical pressure=4600-kPa) at-40°C-and 6500-kPa. Use the-bisection method to determine the mass of CNG in the tank-if the tank volume is 3.5 m³. (Hint: Derive the- abovementioned equation to form-0 = f(v,a, b,T,R), use VL=0.01 m³/kg as the lower bound- and vu=0.02 m³/kg as the upper bound, and perform the iteration until the approximate error less then-10%).1 %3D %3D

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The relationship between pressure (in kPa), temperature (in Kelvin), and the specific volume (in-
m/kg) ofa gas can-be expressed by the Redlich-Kwong equation of state as follows:¶
RT
p =
a
v - b v(v+ b)VT"
Where R=universal-gas constant (0.518 kJ/kg.K), a = 0.427R?T?* /Pc, dan-b =
0.0866R T./ Pe; Wwhere T, and-p, are critical temperature and the critical pressure of the gas,
respectively.
The transportation of compressed natural gas (CNG)'usesa special tank that can withstand high-
pressure and ·low temperature. Assume that the CNG-contains-100% methane (critical-
temperature =191-K, critical pressure=4600-kPa) at -40°C and 6500-kPa. Use the-bisection
method to determine the mass of CNG-in the tank-if the tank volume is 3.5-m³. (Hint: Derive the-
abovementioned-equation to form-0 =f(v,a,b,T,R),use VL=0.01 m³/kg-as the lower bound-
and vu=0.02 m/kg as the upper-bound, and perform the iteration until the approximate error less-
then 10%).
Transcribed Image Text:The relationship between pressure (in kPa), temperature (in Kelvin), and the specific volume (in- m/kg) ofa gas can-be expressed by the Redlich-Kwong equation of state as follows:¶ RT p = a v - b v(v+ b)VT" Where R=universal-gas constant (0.518 kJ/kg.K), a = 0.427R?T?* /Pc, dan-b = 0.0866R T./ Pe; Wwhere T, and-p, are critical temperature and the critical pressure of the gas, respectively. The transportation of compressed natural gas (CNG)'usesa special tank that can withstand high- pressure and ·low temperature. Assume that the CNG-contains-100% methane (critical- temperature =191-K, critical pressure=4600-kPa) at -40°C and 6500-kPa. Use the-bisection method to determine the mass of CNG-in the tank-if the tank volume is 3.5-m³. (Hint: Derive the- abovementioned-equation to form-0 =f(v,a,b,T,R),use VL=0.01 m³/kg-as the lower bound- and vu=0.02 m/kg as the upper-bound, and perform the iteration until the approximate error less- then 10%).
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