Question

A 60.00 L fuel tank is filled with gasoline on a –$10°C$day, then rolled into a storage shed where the temperature is $20°C$. If the tank is not vented, what minimum volume needs to be left empty at filling time so that the tank doesn’t rupture as it warms?

Short answer

The minimum volume of 1.7 L. needs to be left empty at filling time so that the tank doesn’t rupture as it warms.

Step-by-step solution

Description 

A 60.00 L fuel tank is filled with gasoline on a – $10°$day, then rolled into a storage shed where the temperature is $20°C$.

The process of thermal expansion occurs when objects are heated as well as expanded. In case the temperature of an object changes through $∆T$, as well as volume changes through $∆V$and the volume's fractional changes $∆V/V$are effective to the temperature's change $∆T$.

Result of finding the minimum volume 

The equation (18.9) in the form is

$\frac{∆V}{V}=\beta ∆T\left(1\right)$

In this case, $\beta$is the coefficient. Table 18.4 effectively gives the coefficient expression of linear for common materials, for instance

$gasoline\beta =9.6\times {10}^{-4\circ }{C}^{-1}$

Equation (1) for $∆V=\beta V∆T$

In this case, V is the initial volume. The temperature effectively changes from $T_1=-10°Cto{T}_2=20°C$

Therefore, the change in temperature is

role="math" localid="1649072092192" $\begin{array}{rcl}∆T& =& T_2-T_1\\ & =& 20°C-(10°C)\\ & =& -30°C\end{array}$

Thus, plug the values of $\beta ,∆V,T$into equation (2)

$\begin{array}{rcl}∆V& =& \beta L∆T\\ & =& (9.6\times {10}^{-4°}{C}^{-1})\left(60L\right)(30°C)\\ & =& 1.7L\end{array}$

Therefore, the minimum volume of 1.7 L. needs to be left empty at filling time so that the tank doesn’t rupture as it warms.