Chapter 13, Problem 16P

To determine

Convert the given sources data in the Table accompanied for the problems 13.14 to 13.20 in the textbook from Billions of kilowatt-hours to Billions of Btu.

Answer to Problem 16P

The given sources data in the Table accompanied for the problems 13.14 to 13.20 in the textbook from Billions of kilowatt-hours to Billions of Btu are tabulated in Table 1.

Explanation of Solution

Given data:

Refer to the problem 13.16 in textbook for the accompanying table.

Formula used:

The value of the $1\frac{\text{Btu}}{\text{s}}$ is,

$1\frac{\text{Btu}}{\text{s}}=1.055\text{kW}$ (1)

Convert 1 hr into seconds,

$1\text{hr=3600}\text{s}$

Rearrange the equation,

$\text{1}\text{s=}\frac{1}{3600}\text{hr}$ (2)

Calculation:

Substitute equation (2) in equation (1),

$\begin{array}{l}1\frac{\text{Btu}}{\frac{1}{3600}\text{hr}}=1.055\text{kW}\\ \text{1}\text{Btu}=\frac{1.055}{3600}\text{kWhr}\\ \text{1}\text{Btu=2}\text{.93}\times {\text{10}}^{-4}\text{kWhr}\end{array}$

Rearrange the equation for the relation between kWhr to Btu.

$\begin{array}{c}\\ \text{1}\text{kWhr}=\frac{1}{\text{2}\text{.93}\times {\text{10}}^{-4}}\text{Btu}\\ \text{=3412}\text{.96}\text{Btu}\end{array}$ (3)

For coal:

All the following calculations of conversion are in Billions.

Coal for the year 1980 is,

${\left(\text{Coal}\right)}_{1980}=1161.562\text{kWhr}$ (4)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (4).

$\begin{array}{c}{\left(\text{Coal}\right)}_{1980}=1161.562\left(\text{3412}\text{.96}\text{Btu}\right)\\ =3964364.6\text{Btu}\end{array}$

Coal for the year 1990 is,

${\left(\text{Coal}\right)}_{1990}=1594.011\text{kWhr}$ (5)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (5).

$\begin{array}{c}{\left(\text{Coal}\right)}_{1990}=1594.011\left(\text{3412}\text{.96}\text{Btu}\right)\\ =5440295\text{Btu}\end{array}$

Coal for the year 2000 is,

${\left(\text{Coal}\right)}_{2000}=1966.265\text{kWhr}$ (6)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (6).

$\begin{array}{c}{\left(\text{Coal}\right)}_{2000}=1966.265\left(\text{3412}\text{.96}\text{Btu}\right)\\ =6710783.79\text{Btu}\end{array}$

Coal for the year 2005 is,

${\left(\text{Coal}\right)}_{2005}=2040.913\text{kWhr}$ (7)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (7).

$\begin{array}{c}{\left(\text{Coal}\right)}_{2005}=2040.913\left(3412.96\text{Btu}\right)\\ =6965554.432\text{ Btu}\end{array}$

Coal for the year 2010 is,

${\left(\text{Coal}\right)}_{2010}=2217.555\text{kWhr}$ (8)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (8).

$\begin{array}{c}{\left(\text{Coal}\right)}_{2010}=2217.555\left(\text{3412}\text{.96}\text{Btu}\right)\\ =7568426.5\text{Btu}\end{array}$

Coal for the year 2020 is,

${\left(\text{Coal}\right)}_{2020}=2504.786\text{kWhr}$ (9)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (9).

$\begin{array}{c}{\left(\text{Coal}\right)}_{2020}=2504.786\left(\text{3412}\text{.96}\text{Btu}\right)\\ =8548734.42\text{Btu}\end{array}$

The coal for the year 2030 is,

${\left(\text{Coal}\right)}_{2030}=3380.674\text{kWhr}$ (10)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (10).

$\begin{array}{c}{\left(\text{Coal}\right)}_{2030}=3380.674\left(3412.96\text{Btu}\right)\\ =11538105.14\text{Btu}\end{array}$

For petroleum:

All the following calculations of conversion are in Billions.

Petroleum for the year 1980 is,

${\left(\text{Petroleum}\right)}_{1980}=245.9942\text{kWhr}$ (11)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (11).

$\begin{array}{c}{\left(\text{Petroleum}\right)}_{1980}=245.9942\left(3412.96\text{Btu}\right)\\ =839568.36\text{Btu}\end{array}$

Petroleum for the year 1990 is,

${\left(\text{Petroleum}\right)}_{1990}=126.6211\text{kWhr}$ (12)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (12).

$\begin{array}{c}{\left(\text{Petroleum}\right)}_{1990}=126.6211\left(3412.96\text{Btu}\right)\\ =432152.74\text{Btu}\end{array}$

Petroleum for the year 2000 is,

${\left(\text{Petroleum}\right)}_{2000}=111.221\text{kWhr}$ (13)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (13).

$\begin{array}{c}{\left(\text{Petroleum}\right)}_{2000}=111.221\left(3412.96\text{Btu}\right)\\ =379592.82\text{Btu}\end{array}$

Petroleum for the year 2005 is,

${\left(\text{Petroleum}\right)}_{2005}=115.4264\text{kWhr}$ (14)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (14).

$\begin{array}{c}{\left(\text{Petroleum}\right)}_{2005}=115.4264\left(3412.96\text{Btu}\right)\\ =393945.68\text{Btu}\end{array}$

Petroleum for the year 2010 is,

${\left(\text{Petroleum}\right)}_{2010}=104.8182\text{BkWhr}$ (15)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (15).

$\begin{array}{c}{\left(\text{Petroleum}\right)}_{2010}=104.8182\left(3412.96\text{Btu}\right)\\ =357740.32\text{Btu}\end{array}$

Petroleum for the year 2020 is,

${\left(\text{Petroleum}\right)}_{2020}=106.6799\text{kWhr}$ (16)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (16).

$\begin{array}{c}{\left(\text{Petroleum}\right)}_{2020}=106.6799\left(3412.96\text{Btu}\right)\\ =364094.23\text{Btu}\end{array}$

Petroleum for the year 2030 is,

${\left(\text{Petroleum}\right)}_{2030}=114.6741\text{kWhr}$ (17)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (17).

$\begin{array}{c}{\left(\text{Petroleum}\right)}_{2030}=114.6741\left(3412.96\text{Btu}\right)\\ =391378.11\text{Btu}\end{array}$

For Natural gas:

All the following calculations of conversion are in Billions.

Natural gas for the year 1980 is,

${\left(\text{Natural}\text{gas}\right)}_{1980}=346.2399\text{kWhr}$ (18)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (18).

$\begin{array}{c}{\left(\text{Natural}\text{gas}\right)}_{1980}=346.2399\left(3412.96\text{Btu}\right)\\ =1181702.92\text{Btu}\end{array}$

Natural gas for the year 1990 is,

${\left(\text{Natural}\text{gas}\right)}_{1990}=372.7652\text{BkWhr}$ (19)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (19).

$\begin{array}{c}{\left(\text{Natural}\text{gas}\right)}_{1990}=372.7652\left(3412.96\text{Btu}\right)\\ =1272232.71\text{Btu}\end{array}$

Natural gas for the year 2000 is,

${\left(\text{Natural}\text{gas}\right)}_{2000}=601.0382\text{kWhr}$ (20)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (20).

$\begin{array}{c}{\left(\text{Natural}\text{gas}\right)}_{2000}=601.0382\left(3412.96\text{Btu}\right)\\ =2051319.33\text{Btu}\end{array}$

Natural gas for the year 2000 is,

${\left(\text{Natural}\text{gas}\right)}_{2005}=751.8189\text{kWhr}$ (21)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (21).

$\begin{array}{c}{\left(\text{Natural}\text{gas}\right)}_{2005}=751.8189\left(3412.96\text{Btu}\right)\\ =2565927.833\text{Btu}\end{array}$

Natural gas for the year 2010 is,

${\left(\text{Natural}\text{gas}\right)}_{2010}=773.8234\text{kWhr}$ (22)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (22).

$\begin{array}{c}{\left(\text{Natural}\text{gas}\right)}_{2010}=773.8234\left(3412.96\text{Btu}\right)\\ =2641028.31\text{Btu}\end{array}$

Natural gas for the year 2020 is,

${\left(\text{Natural}\text{gas}\right)}_{2020}=1102.762\text{kWhr}$ (23)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (23).

$\begin{array}{c}{\left(\text{Natural}\text{gas}\right)}_{2020}=1102.762\left(3412.96\text{Btu}\right)\\ =3763682.59\text{Btu}\end{array}$

Natural gas for the year 2030 is,

${\left(\text{Natural}\text{gas}\right)}_{2030}=992.7706\text{BkWhr}$ (24)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (24).

$\begin{array}{c}{\left(\text{Natural}\text{gas}\right)}_{2030}=992.7706\left(3412.96\text{Btu}\right)\\ =3388286.34\text{Btu}\end{array}$

For Nuclear:

All the following calculations of conversion are in Billions.

Nuclear of the year 1980 is,

${\left(\text{Nuclear}\right)}_{1980}=251.1156\text{kWhr}$ (25)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (25).

$\begin{array}{c}{\left(\text{Nuclear}\right)}_{1980}=251.1156\left(3412.96\text{Btu}\right)\\ =857047.49\text{Btu}\end{array}$

Nuclear of the year 1990 is,

${\left(\text{Nuclear}\right)}_{1990}=576.8617\text{kWhr}$ (26)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (26).

$\begin{array}{c}{\left(\text{Nuclear}\right)}_{1990}=576.8617\left(3412.96\text{Btu}\right)\\ =1968805.9\text{Btu}\end{array}$

Nuclear of the year 2000 is,

${\left(\text{Nuclear}\right)}_{2000}=753.8929\text{kWhr}$ (27)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (27).

$\begin{array}{c}{\left(\text{Nuclear}\right)}_{2000}=753.8929\left(3412.96\text{Btu}\right)\\ =2573006.31\text{Btu}\end{array}$

Nuclear of the year 2005 is,

${\left(\text{Nuclear}\right)}_{2005}=774.0726\text{kWhr}$ (28)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (28).

$\begin{array}{c}{\left(\text{Nuclear}\right)}_{2005}=774.0726\left(3412.96\text{Btu}\right)\\ =2641878.820\text{Btu}\end{array}$

Nuclear of the year 2010 is,

${\left(\text{Nuclear}\right)}_{2010}=808.6948\text{kWhr}$ (29)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (29).

$\begin{array}{c}{\left(\text{Nuclear}\right)}_{2010}=808.6948\left(3412.96\text{Btu}\right)\\ =2760043\text{Btu}\end{array}$

Nuclear of the year 2020 is,

${\left(\text{Nuclear}\right)}_{2020}=870.698\text{kWhr}$ (30)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (30).

$\begin{array}{c}{\left(\text{Nuclear}\right)}_{2020}=870.698\left(3412.96\text{Btu}\right)\\ =2971657.44\text{Btu}\end{array}$

Nuclear of the year 2030 is,

${\left(\text{Nuclear}\right)}_{2030}=870.5909\text{kWhr}$ (31)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (31).

$\begin{array}{c}{\left(\text{Nuclear}\right)}_{2030}=870.5909\left(3412.96\text{Btu}\right)\\ =2971291.91\text{Btu}\end{array}$

For Renewable/Others:

All the following calculations of conversion are in Billions.

Renewable of the year 1980 is,

${\left(\text{Renewable}\right)}_{1980}=284.6883\text{kWhr}$ . (32)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (32).

$\begin{array}{c}{\left(\text{Renewable}\right)}_{1980}=284.6883\left(3412.96\text{Btu}\right)\\ =971629.78\text{Btu}\end{array}$

Renewable of the year 1990 is,

${\left(\text{Renewable}\right)}_{1990}=357.2381\text{kWhr}$ (33)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (33).

$\begin{array}{c}{\left(\text{Renewable}\right)}_{1990}=357.2381\left(3412.96\text{Btu}\right)\\ =1219239.46\text{Btu}\end{array}$

Renewable of the year 2000 is,

${\left(\text{Renewable}\right)}_{2000}=356.4786\text{kWhr}$ (34)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (34).

$\begin{array}{c}{\left(\text{Renewable}\right)}_{2000}=356.4786\left(3412.96\text{Btu}\right)\\ =1216647.203\text{Btu}\end{array}$

Renewable of the year 2005 is,

${\left(\text{Renewable}\right)}_{2005}=375.8663\text{kWhr}$ (35)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (35).

$\begin{array}{c}{\left(\text{Renewable}\right)}_{2005}=375.8663\left(3412.96\text{Btu}\right)\\ =1282816.647\text{Btu}\end{array}$

Renewable of the year 2010 is,

${\left(\text{Renewable}\right)}_{2010}=475.7432\text{kWhr}$ (36)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (36).

$\begin{array}{c}{\left(\text{Renewable}\right)}_{2010}=475.7432\left(3412.96\text{Btu}\right)\\ =1623692.51\text{Btu}\end{array}$

Renewable of the year 2020 is,

${\left(\text{Renewable}\right)}_{2020}=515.1523\text{kWhr}$ (37)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (37).

$\begin{array}{c}{\left(\text{Renewable}\right)}_{2020}=515.1523\left(3412.96\text{Btu}\right)\\ =1758194.19\text{Btu}\end{array}$

Renewable of the year 2030 is,

${\left(\text{Renewable}\right)}_{2030}=559.1335\text{kWhr}$ (38)

Substitute $\text{3412}\text{.96}\text{Btu}$ for $\text{1}\text{kWhr}$ in equation (38).

$\begin{array}{c}{\left(\text{Renewable}\right)}_{2030}=559.1335\left(3412.96\text{Btu}\right)\\ =1908300.27\text{Btu}\end{array}$

Therefore, the conversion from the Billions of kilowatt-hours to Billions of Btu is tabulated in Table 1 as below,

Table 1

Year	Coal	Petroleum	Natural Gas	Nuclear	Renewable/Other
1980	3964364.644	839568.365	1181702.929	857047.498	971629.780
1990	5440295.783	432152.749	1272232.717	1968805.908	1219239.346
2000	6710783.794	379592.824	2051319.335	2573006.312	1216647.203
2005	6965554.432	393945.686	2565927.833	2641878.821	1282816.647
2010	7568426.513	357740.324	2641028.311	2760043.005	1623692.512
2020	8548734.427	364094.232	3763682.596	2971657.446	1758194.194
2030	11538105.135	391378.116	3388286.347	2971291.918	1908300.270

Conclusion:

Hence, the conversion for the energy sources from billions kilowatt-hours to billion Btu has been explained.