Question

When $1.0g$ of gasoline burns, it releases $11kcal$. The density of gasoline is$0.74g/mL$. $(3.4,3.6)$

$\left(a\right)$ How many megajoules are released when $1.0gal$ of gasoline burns?

$\left(b\right)$If a television requires$150kJ/h$ to run, how many hours can the television run on the energy provided by $1.0gal$ of gasoline?

Short answer

Part $\left(a\right)$

$\left(a\right)$The gasoliene burns when $128.65\mathrm{MJ}$are released.

Part $\left(b\right)$

$\left(b\right)$The gasoliene energy needs $n=900hrs$to run.

Step-by-step solution

Step: 1 Given Information: (Part a)

Given data are: $1.0gal$gasoliene and $11kcal$of energy and role="math" localid="1651856436534" $0.74g/mL$gasoliene density,

To find the quantity of megajoules released.

Step: 2 Finding energy: (Part a) 

The density as $0.74g/ml$

$\text{volume}=\frac{\text{Mass}}{\text{Density}}$

$Volume==\frac{1.0\mathrm{g}}{0.74\mathrm{g}/\mathrm{ml}}$

$Volume=1.35\mathrm{mL}$

Energy as

$E=11\mathrm{kcal}\times 4.184$

$E=42.024kJ.$

Step: 3 Finding megajoules: (Part a) 

The energy of gasoliene burns at

$\begin{array}{l}=\frac{3773.6\mathrm{mL}\times 46.024\mathrm{kJ}}{1.35\mathrm{mL}}\text{of energy}\\ =128649.01\mathrm{kJ}\\ =128.65\mathrm{MJ}.\end{array}$

As a result,the energy released isrole="math" localid="1651856924121" $128.65\mathrm{MJ}.$

Step: 2 Given Information: (Part b)

Given data are: $150KJ/h$and $1.0gal$of gasoliene and $11kcal$of energy and $0.74g/mL$gasoliene density, .

To find the number of hours required to run television.

Step: 5 Finding number of hours: (Part b)

Energy needed $300KJ$to run $2hrs.$

The number of hours as,

$n=\frac{1.35\times {10}^5\times 2}{300}$

$n=900hrs.$

As a result,the number of hours needed is$n=900hrs.$