Q. 1.52 - An Introduction to Thermal Physics

Question

The enthalpy of combustion of a gallon ($3.8$ liters) of gasoline is about $31,000 kcal$. The enthalpy of combustion of an ounce $\left(28 g\right)$ of corn flakes is about$100 kcal$. Compare the cost of gasoline to the cost of corn flakes, per calorie.

Step-by-Step Solution

Answer

The cost of gasoliene is ${\text{ Rate }}_{\text{gasoline }}=0.009\text{ cents }/\mathrm{kcal}$ to the cost of corn flakes is ${\text{ Rate }}_{\text{corn }}=1.14\text{ cents }/\mathrm{kcal}.$

Step: 1 Definition of Enthalpy:

The enthalpy change that happens when one mole of a material is created from its component elements in their standard states is known as the standard enthalpy of formation. The standard enthalpy of production of a substance known in its initial state is zero.

Step: 2 Finding entalpy:

To compare the prices of gasoline and corn flakes, we must look at the price per kcal. First, the average price of a gallon of gasoline in $2018$is roughly $\$2.79$; one gallon of gasoline has an enthalpy of $31000kcal$, hence the price per$kcal$ is:$\$$ Rate Gasoliene $= \frac{ \$2.79}{31000kca}=0.009 cents/kcal$ Rate gasoliene$=0.009 cents/kcal$ used $\$1.00=100 cents$ as an example. The cheapest corn flake (which I discovered on the internet - Kellogg's brand-) costs $\$20.45$ and weighs $18$ ounces, thus one ounce costs $\$1.14.$ An ounce of corn flakes has an enthalpy of $100kcal$, and so the price per $kcal$ is:

$$\begin{gathered} Rat{e}_{Corn}=\frac{\mathrm{\$}1.14}{100\mathrm{kcal}} \\ Rat{e}_{Corn}=1.14 cents/kcal. \end{gathered}$$

The enthalpy price for $1 cal$ of fakes is $100$ times higher than the price of $1cal$ of Gasoliene enthalpy.