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If the temperature $T$ of a solid or liquid of volume $V$ is changed by an amount $\Delta T,$ then the volume will change by the amount $\Delta V=\beta V \Delta T,$...

Question

If the temperature $T$ of a solid or liquid of volume $V$ is changed by an amount $\Delta T,$ then the volume will change by the amount $\Delta V=\beta V \Delta T,$ where $\beta$ is called the coefficient of volume expansion. For moderate changes in temperature $\beta$ is taken as constant. Suppose that a tank truck loads 4000 gallons of ethyl alcohol at a temperature of $35^{\circ} \mathrm{C}$ and delivers its load sometime later at a temperature of $15^{\circ} \mathrm{C} .$ Using $\beta=7.5 \t

If the temperature $T$ of a solid or liquid of volume $V$ is changed by an amount $\Delta T,$ then the volume will change by the amount $\Delta V=\beta V \Delta T,$ where $\beta$ is called the coefficient of volume expansion. For moderate changes in temperature $\beta$ is taken as constant. Suppose that a tank truck loads 4000 gallons of ethyl alcohol at a temperature of $35^{\circ} \mathrm{C}$ and delivers its load sometime later at a temperature of $15^{\circ} \mathrm{C} .$ Using $\beta=7.5 \times 10^{-4} /^{\circ} \mathrm{C}$ for ethyl alcohol, find the number of gallons delivered.



Answers

A steel tank is completely filled with 1.90 m$^3$of ethanol when both the tank and the ethanol are at 32.0$^\circ$C. When the tank and its contents have cooled to 18.0$^\circ$C, what additional volume of ethanol can be put into the tank?


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