Question

The density of gasoline is 7.30 x 102 kg/m3 at 0°C. Its average coefficient of volume expansion is 9.60 x 104 (c), and note that 1.00 gal 0.00380 m3 (a) Calculate the mass of 11.6 gal of gas at 0°C. (Give your answer to at least two decimal places.) kg (b) tr 1.000 m3 of gasoline at ОС is warmed by 21.2.С, calculate its new volume. (Give your answer to at least two decimal places.) m3 (e) Using the answer to part (b), calculate the density of gasoline at 21.2°C. (Give your answer to at least three significant figures.) kg/m (d) Calculate the mass of 13.6 gal of gas at 21.2 C. (Give your answer to at least two decimal places) (e) How many extra kilograms of gasoline would you get if you bought 11.6 gal of gasoline at О.С rather than at 21.2C from a pump that is not temperature kg Need Help?

Answer 1

Solution :-

a )

The density of gasoline is 7.30 ✕ 10² kg/m³ = $\rho$

volume V = 11.6 gal = 11.6× 0.0038 = 0.04408

mass = density X volume

m = $\rho$ X V

m = 7.30 ✕ 10² X 0.04408

m = 32.178 kg

b )

volume expansion is 9.60 ✕ 10⁻⁴ (°C)⁻¹ = $\alpha$

dt = 22.5

V₂ = V₁ ( 1 + $\alpha$ dt )

V₂ = 1 X ( 1 + 9.60 ✕ 10⁻⁴ X 21.2 )

V₂ = 1.02035 m³  

c )

denisty = mass / V₂

= $\rho$ X V₁ / V₂

= 7.30 ✕ 10² X 1 / 1.02035

density = 715.4407 kg/m³

d )

mass m₁ = $\rho$ X V_o

= 715.4407 X 11.6 X 0.0038

mass m₁ = 31.537kg

e )

$\rho$m = m₀ - m₁

= 32.178 - 31.537

$\rho$m = 0.641 kg