Question

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

Short 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-by-step solution

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 Gasolienerole="math" localid="1650287339371" $=\frac{\$2.79}{31000kca}=0.009cents/kcal$Rate gasoliene$=0.009cents/kcal$used $\$1.00=100cents$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:

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

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