If 140 ft^3 of methane gas at 60 degree celcius and 1 atm is equivalent to 1 gal of gasoline,what would be the

Question

if 140 ft^3 of methane gas at 60 degree fahrenheit and 1 atm is equivalent to 1 gal of gasoline,what would be volume of the tank required to hold methane at 3000 psia and 60 degree fahrenheit in an amount equivalent to 10 gal of gasoline?

Answer 1

Let:

V1 = volume of methane equivalent to 10 gal of gasoline at 60 degrees F at 1 atmosphere(14.7 psi)

p1 =14.7 psia

p2 =3000psia

V2 = volume of methane at 3000psia

T1 = T2 = 60 degrees fahrenheit

V1 =140 x 10 = 1400 ft^3

p1V1/T1 = p2V2/T2

14.7 x 1400/60 = 3000 V2/60

V2 = 14.7 x 1400/3000 = 6.86 ft^3

Answer 2

if 140 ft^3 of methane gas at 60 degree celcius and 1 atm is equivalent to 1 gal of gasoline,  then:

1400 ft^3 of methane gas at 60 degree celcius and 1 atm is equivalent to 10 gal of gasoline

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P1V1T2 = P2V2T1

at constant temp becomes, & 1 atm = 14.7 psi:

P1V1 = P2V2

(1atm)(1400 cu ft) = (3000 psia)(V2)

(14.7 psia)(1400 cu ft) = (3000 psia)(V2)

V2 = 6.86 cu ft

& @ 7.480 gallons / cu ft , that's 51.3 gallons

your answers are: 6.86 ft^3  or 51.3 gallons

@ 2 sig figs that becomes  6.9 ft^3  or 51 gallons