Chapter 9, Problem 57E

Interpretation Introduction

Interpretation:

Increase in energy consumption between $1949$ and $2012$ is to be estimated and the average yearly increase during this period is to determined. The increase in energy production between $1949$ and $2012$ is to be estimated and the average yearly increase during this period is to be determined. The gap between the production and the consumption in $2012$ are to be calculated.

Concept Introduction:

Energy is the property that is required by an object to perform work and to heat itself and it can be measured.

The average change is calculated by dividing the change in the value by the elapsed time.

Answer to Problem 57E

Solution:

a)

The energy consumption between $1949$ and $2012$ is $0.952\text{quad}/\text{yr}$.

b)

The energy production between $1949$ and $2012$ is $0.71quad/yr$.

c)

The gap between production and consumption in $2012$ is $-15\text{quad}/\text{yr}$.

Explanation of Solution

a) The increase in the energy consumption between 1949 and 2012 and the average yearly increase during this period.

The energy consumption in $1949\text{is}3\text{5}\text{quad}$ and in $2012\text{is}95\text{quad}$.

The average energy consumption between $1949$ and $2012$ is calculated as follows:

The energy consumption in $1949\text{is}3\text{5}\text{quad}$ and in $2012\text{is}95\text{quad}$.

$\text{The}\text{yearly}\text{average}\text{consumption}=\frac{\text{Energy}\text{consumption}\text{in}2012-\text{Energy}\text{consumption}\text{in}1949}{2012-1949}$

Substitute the value of energy consumption in $1949$ and $2012$ in the above expression.

$\begin{array}{l}\text{The}\text{yearly}\text{average}\text{consumption}=\left(\frac{95\text{quad}-35\text{quad}}{2012\text{yr}-1949\text{yr}}\right)\\ =\left(\frac{60\text{quad}}{63\text{yr}}\right)\\ =0.952\text{quad}\text{/}\text{yr}\end{array}$

Hence, the average yearly energy consumption between $1949$ and $2012$ is,

$0.952\text{quad}/\text{yr}$.

b) The increase in energy production between 1949 and 2012 and average yearly increase during this period.

The energy production in $1949\text{is}3\text{5}\text{quad}$ and in $2012\text{is}80\text{quad}$.

The average energy production between $1949$ and $2012$ is calculated as follows:

The energy production in $1949\text{is}3\text{5}\text{quad}$ and in $2012\text{is}80\text{quad}$.

$\text{The}\text{yearly}\text{average}\text{production}=\frac{\text{Energy}\text{production}\text{in}2012-\text{Energy}\text{production}\text{in}1949}{2012-1949}$

Substitute the value of energy production in $1949$ and $2012$ in the above expression.

$\begin{array}{c}\text{The}\text{yearly}\text{average}\text{production}=\left(\frac{80-35}{2012-1949}\right)\\ =\left(\frac{45}{63}\right)\\ =0.71quad/yr\end{array}$

Hence, the energy production between $1949$ and $2012$ is $0.71quad/yr$.

c) The gap between production and consumption in 2012.

The gap between production and consumption in $2012$.

The gap between production and consumption in $2012$ is calculated as follows:

$\text{The}\text{gap}\text{between}\text{production}\text{and}\text{consumption}=\left(\begin{array}{c}\text{The energy production}\text{in 2012}-\\ \text{The energy consumption in 2012}\end{array}\right)$.

Substitute the value of energy production and energy consumption in the above expression.

$\begin{array}{c}\text{The}\text{gap}\text{between}\text{production}\text{and}\text{consumption}=\left(80-95\right)\\ =-15\text{quad}/\text{yr}\end{array}$

Hence, the gap between production and consumption in $2012$ is $-15\text{quad}/\text{yr}$.

Conclusion

The energy consumption between $1949$ and $2012$, the energy production between $1949$ and $2012$ is $0.952\text{quad}/\text{yr}$, and the gap between the production and the consumption in $2012$ is $-15\text{quad}/\text{yr}$.