The density of gasoline is 7.30 102 kg/m 3 at 0°C. Its average coefficient of vo
ID: 1463577 • Letter: T
Question
The density of gasoline is 7.30 102 kg/m3 at 0°C. Its average coefficient of volume expansion is 9.60 104 (°C)-1, and note that 1.00 gal = 0.00380 m3.
(a) Calculate the mass of 11.4 gal of gas at 0°C. (Give your answer to at least two decimal places.)
(b) If 1.000 m3 of gasoline at 0°C is warmed by 17.7°C, calculate its new volume. (Give your answer to at least two decimal places.)
(c) Using the answer to part (b), calculate the density of gasoline at 17.7°C. (Give your answer to at least three significant figures.)
(d) Calculate the mass of 11.4 gal of gas at 17.7°C. (Give your answer to at least two decimal places.)
(e) How many extra kilograms of gasoline would you get if you bought 11.4 gal of gasoline at 0°C rather than at 17.7°C from a pump that is not temperature compensated?
Explanation / Answer
density do = 7.32*10^2 kg/m^3
(a)
volume = vo = 11.4 gal = 11.4*0.0038
mass = mo = do*vo = 730*11.4*0.0038 = 31.63 kg
(b)
v2 = v1*(1+(alfa*dt))
v2 = 1*(1+(9.6*10^-4*17.7))
v2 = 1.017 m^3
(c)
density d1 = mass/v2 = (do*v1)/v2 = (730*1)/1.017 = 717.80 kg/m^3
(d)
mass m1 = d1*vo = 717.80* 11.4*0.0038 = 31.10 kg
(e)
dm = mo-m1 = 31.63-31.10 = 0.53 kg <<-----------answer