Exemplo 13.5 de College Physics, 13.2 Thermal Expansion of Solids and Liquids

Calculating Thermal Stress: Gas Pressure

Problema e solução em inglês, como no livro original.

What pressure would be created in the gasoline tank considered in Example 13.4, if the gasoline increases in temperature from $15.0 º C$ to $35.0 º C$ without being allowed to expand? Assume that the bulk modulus $B$ for gasoline is $1 . 00 \times 10^{9} {N/m}^{2}$ . (For more on bulk modulus, see Elasticity: Stress and Strain.)

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Estratégia
To solve this problem, we must use the following equation, which relates a change in volume $Δ V$ to pressure:
$Δ V = \frac{1}{B} \frac{F}{A} V_{0},$
13.15

where $F / A$ is pressure, $V_{0}$ is the original volume, and $B$ is the bulk modulus of the material involved. We will use the amount spilled in Example 13.4 as the change in volume, $Δ V$ .
Solução
1. Rearrange the equation for calculating pressure:

$P = \frac{F}{A} = \frac{Δ V}{V_{0}} B .$
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2. Insert the known values. The bulk modulus for gasoline is $B = 1 . 00 \times 10^{9} {N/m}^{2}$ . In the previous example, the change in volume $Δ V = 1 . 10 L$ is the amount that would spill. Here, $V_{0} = 60 . 0 L$ is the original volume of the gasoline. Substituting these values into the equation, we obtain
$P = \frac{1 . 10 L}{60 . 0 L} (1 . 00 \times 10^{9} Pa) = 1 . 83 \times 10^{7} Pa .$
13.17
Discussão
This pressure is about $2500 {lb/in}^{2}$ , much more than a gasoline tank can handle.

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