Question

A tank truck was filled with 45,725 L of gasoline in Peshawar where the temperature was 28.0°C. The gasoline was delivered to Swat where the temperature was -12°C. Volume expansion coefficient of Gasoline is 950×10-6 °C-1.
Find out the amount of gasoline delivered in litres
Infer the volume of the gasoline due to changed temperature

Answer 1

Answer on Question #63924, Physics / Optics

A tank truck was filled with 45,725 L of gasoline in Peshawar where the temperature was 28.0°C. The gasoline was delivered to Swat where the temperature was -12°C. Volume expansion coefficient of Gasoline is 950×10⁻⁶ °C⁻¹. Find out the amount of gasoline delivered in litres. Infer the volume of the gasoline due to changed temperature

Find: V₂ - ? ΔV - ?

Given:

V₁ = 45.725 L

t₁ = 28.0°C

t₂ = -12°C

β = 950 × 10⁻⁶ °C⁻¹

Solution:

Increase of the volume:

V₁ = V₀(1 + βt₁)(1),

where V₀ is volume of gasoline at temperature t = 0°C,

V₁ is volume of gasoline at temperature t₁

Of (1) ⇒ V₀ = (V₁ / (1 + βt₁)) (2)

Of (2) ⇒ V₀ = 44.5403 L (3)

Reduction of the volume:

V₂ = V₀(1 + βt₂)(4),

where V₀ is volume of gasoline at temperature t = 0°C,

V₂ is volume of gasoline at temperature t₂

(3) in (4): V₂ = 44.0326 L (5)

Change of volume:

ΔV = V₂ - V₁ (6),

where V₁ = 45.725 L

(5) in (6): ΔV = -1.6924 L

Answer:

Find out the amount of gasoline delivered in litres

44.0326 L

Infer the volume of the gasoline due to changed temperature

decreased by 1.6924 L

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