Chapter 13.4, Problem 42PP

(a)

To determine

Liters of gasoline delivered by the truck.

Answer to Problem 42PP

Truck delivers $\text{ 4}{\text{.4 × 10}}^{\text{4}}\text{L}$ gasoline.

Explanation of Solution

Given:

Co-efficient of volume Expansion $\beta \text{=}{\text{950×10}}^{\text{-6}}{\text{°C}}^{\text{-1}}$

Volume at beginning ${\text{V}}_1\text{=}\text{45,725}\text{L}$

Change in temperature $\Delta T=\left(\text{-12}\text{.0°C-28}\text{.0°C}\right)$

Formula used:

Co-efficient of volume Expansion, $\beta$ , is the change in volume divided by the original volume and the change in temperature. Mathematical expression is $\beta \text{=}\frac{\Delta V}{V_1\Delta T}$ or $\beta \text{=}\frac{V_2-V_1}{V_1\Delta T}$

Where, $\Delta V$ , change in volume

  $\Delta T$ , change in temperature

  $V_1$ , Initial volume

Calculation:

Expand the formula, $\beta \text{=}\frac{V_2-V_1}{V_1\Delta T}$ , So, $V_2=\beta V_1\Delta T+V_1$

Now, put the given values:

  $V_2=\left({\text{950×10}}^{\text{-6}}{\text{°C}}^{\text{-1}}\right)\left(\text{45,725}\text{L}\right)\left(\text{-12}\text{.0°C-28}\text{.0°C}\right)\text{+}\left(\text{45,725}\text{L}\right)$

  ${\text{V}}_{\text{2}}\text{= 4}{\text{.4 × 10}}^{\text{4}}\text{L}$

Conclusion: $\text{ 4}{\text{.4 × 10}}^{\text{4}}\text{L}$ is delivered by the truck.

(b)

To determine

Change in gasoline

Answer to Problem 42PP

As the truck moved to colder region, volume of gasoline reduced, but the mass remains the same.

Explanation of Solution

Introduction: Gasoline is a mixture of volatile and also, flammable liquid hydrocarbon. It is derived from petroleum. Also, it is used for internal-combustion engines.

Change in gasoline is dependent on the temperature. The colder the liquid, the denser it gets. Thus, as the truck filled with gasoline moved from $\text{28°C}$ to $\text{-12°C}$ , its volume decreased as it turns denser. However, the energy content remains the same.

Hence, volume of gasoline reduced because the temperature decreased. Also, the mass of the gasoline remained the same.

Conclusion: Gasoline got denser as its volume also decreased, but the mass remained same.