Chapter 9, Problem 9.16PAE

9.16 According to Figure 9.2, the total energy supply in the United States in 2016 was $\text{111}.\text{26}\times \text{1}{0}^{\text{15}}$ Btu. Express this value in joules and in calories.

FIGURE 9.2 Energy production and consumption (in quadrillion Btu) in the United States during the year 2016. The discussion in the text explains how to read this complex figure, which contains an enormous amount of information about the energy economy. Data come from the Department of Energy and do not always add up exactly as expected due to rounding and other issues.

Interpretation Introduction

Interpretation: The total energy supply in the United States in the year 2016 was $111.26\times {10}^{15}Btu$. Express the value of energy in Joules and in Calories

Concept Used: Given below are the conversion rules:

$1Btu=\text{ 252}\text{.055 }Calories$

$1Btu=\text{ 1055}\text{.06 }Joules$

Answer to Problem 9.16PAE

Solution: $1Btuofenergyisequalto \text{ 28043}\text{.7 }\times {10}^{15}Calories$ and $1Btuofenergyisequalto \text{ 122660}\text{.7 }\times {10}^{15}Joules$

Given: The total energy supply in the United States in the year 2016 was $111.26\times {10}^{15}Btu$.

Explanation of Solution

We know that

$1Btu=\text{ 252}\text{.055 }Calories$

Thus, we have two possible conversion factors as follows:

• $\frac{1Btu}{\text{252}\text{.055 }Calories}$ and $\frac{\text{252}\text{.055 }Calories}{1Btu}$

  Now, Amount of Energy in Btu = $111.26\times {10}^{15}Btu$

  Using the above conversion factor, the amount of energy in Calories is given as follows:

  Amount of Energy $=111.26\times {10}^{15}Btu\times \frac{\text{252}\text{.055 }Calories}{1Btu}$

  Thus, the amount of Energy $=\text{ 28043}\text{.7 }\times {10}^{15}Calories$

  Also,

  We know that

  $1Btu=\text{ 1055}\text{.06 }Joules$

  Thus, we have two possible conversion factors as follows:

  $\frac{1Btu}{\text{1055}\text{.06 }Joules}$ and $\frac{\text{1055}\text{.06 }Joules}{1Btu}$

  Now, Amount of Energy in Btu = $111.26\times {10}^{15}Btu$

  Using the above conversion factor, the amount of energy in Calories is given as follows:

  Amount of Energy $=111.26\times {10}^{15}Btu\times \frac{\text{1055}\text{.06 }Joules}{1Btu}$

  Thus, the amount of Energy $=\text{ 122660}\text{.7 }\times {10}^{15}Joules$

Conclusion

Thus, we have

$111.26\times {10}^{15}Btuofenergy=\text{ 28043}\text{.7 }\times {10}^{15}Caloriesofenergy$

$111.26\times {10}^{15}Btuofenergy=\text{122660}\text{.7 }\times {10}^{15}Joulesofenergy$