Um pequeno tanque, completamente preenchido com 20,0ell de gasolina a 0°F, é logo a seguir transferido para uma garagem mantida à temperatura de 70°F. Sendo γ = 0,0012°C^{-1} o coeficiente de expansão volumétrica da gasolina, a alternativa que melhor expressa o volume de gasolina que vazará em conseqüência do seu aquecimento até a temperatura da garagem é

Alright, let's break down the problem step by step!

The question asks us to find the volume of gasoline that will spill out of the tank when it's transferred to a garage with a temperature of 70°F. We're given the initial temperature of the gasoline as 0°F and the volume of the tank as 20.0 liters. We're also given the coefficient of volumetric expansion of gasoline as γ = 0.0012°C⁻¹.

First, let's convert the initial temperature from Fahrenheit to Celsius: 0°F = -17.78°C. Now, we can use the formula for thermal expansion of a substance:

V₂ = V₁(1 + γΔT)

where V₁ is the initial volume, V₂ is the final volume, γ is the coefficient of volumetric expansion, and ΔT is the change in temperature. Plugging in the values, we get:

V₂ = 20.0(1 + 0.0012(70 - (-17.78)))

Simplifying the equation, we get:

V₂ ≈ 20.94 liters

So, the volume of gasoline that will spill out of the tank is the difference between the final volume and the initial volume:

ΔV = V₂ - V₁ ≈ 20.94 - 20.0 ≈ 0.940 liters

Therefore, the correct answer is B) 0.940 liters.

Explanation: The key to this problem is to recognize that the volume of the gasoline will increase as it's heated from 0°F to 70°F. We can use the formula for thermal expansion to find the final volume of the gasoline, and then subtract the initial volume to find the volume that will spill out of the tank.