Please show all Steps and Graphs 1000 kg of natural gas at 100 bar and 255 K is

Question

Please show all Steps and Graphs
1000 kg of natural gas at 100 bar and 255 K is stored in a tank. If the pressure
p, specific volume v and temperature T of the gas are related by the following expression (the teacher gave us the answer to be 8.84 m^3):

[5.18x 10 ^-3 T(v-.002668)] -8.91 x 10^-3/v^2

where v is in m^3/Kg, T is in Kelvin and p is bar, determine the volume of gas in the tank. Also plot pressure versus v and T for the isotherms T = 250, 500 and 1000 K.
Note that the numbers in the above expression have their own units.

Explanation / Answer

100,000 N/m² = [(5.18 × 10³)(255K)/(v - 0.002668)] - (8.91 × 10³)/v²

100,000 = (1.3209)/(v - 0.002668) - (8.91 × 10³)/v²

100,000v²(v - 0.002668) = 1.3209v² - (8.91 × 10³)(v - 0.002668)

100,000v³ - 266.8v² = 1.3209v² - 8.91 × 10³v + 0.00002377188

100,000v³ - 268.1209v² + 8.91 × 10³v - 0.00002377188 = 0

I used the solver here:

v = 0.00268105 m³/kg

So, if I didn't mess up, the actual volume should be:

V = 100kg × 0.00268105 m³/kg = 0.0268105 m³

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