To determine which list correctly orders the fuels by increasing heat per dollar, we need to first calculate the heat per dollar for each fuel. This is done by dividing the heat of combustion (negative value indicating energy released) by the cost per gram.
Given data:
[tex]\[
\begin{aligned}
&\text{charcoal: } \frac{-35 \text{ kJ/g}}{0.06 \text{ \$}} \\
&\text{coal: } \frac{-30 \text{ kJ/g}}{0.06 \text{ \$}} \\
&\text{gasoline: } \frac{-34 \text{ kJ/g}}{0.06 \text{ \$}} \\
&\text{kerosene: } \frac{-37 \text{ kJ/g}}{0.06 \text{ \$}} \\
&\text{natural gas: } \frac{-50 \text{ kJ/g}}{0.06 \text{ \$}} \\
&\text{wood: } \frac{-20 \text{ kJ/g}}{0.06 \text{ \$}} \\
\end{aligned}
\][/tex]
Calculating the heat per dollar for each fuel:
1. Charcoal:
[tex]\[
\frac{-35 \text{ kJ/g}}{0.06 \text{ \$}} = -583.33 \text{ kJ/\$}
\][/tex]
2. Coal:
[tex]\[
\frac{-30 \text{ kJ/g}}{0.06 \text{ \$}} = -500.00 \text{ kJ/\$}
\][/tex]
3. Gasoline:
[tex]\[
\frac{-34 \text{ kJ/g}}{0.06 \text{ \$}} = -566.67 \text{ kJ/\$}
\][/tex]
4. Kerosene:
[tex]\[
\frac{-37 \text{ kJ/g}}{0.06 \text{ \$}} = -616.67 \text{ kJ/\$}
\][/tex]
5. Natural Gas:
[tex]\[
\frac{-50 \text{ kJ/g}}{0.06 \text{ \$}} = -833.33 \text{ kJ/\$}
\][/tex]
6. Wood:
[tex]\[
\frac{-20 \text{ kJ/g}}{0.06 \text{ \$}} = -333.33 \text{ kJ/\$}
\][/tex]
Next, we order these fuels from the least negative (lowest magnitude) to the most negative (highest magnitude) heat per dollar values, since a higher magnitude negative value indicates more heat per dollar.
Ordered list:
1. Wood: -333.33 kJ/\[tex]$
2. Coal: -500.00 kJ/\$[/tex]
3. Gasoline: -566.67 kJ/\[tex]$
4. Charcoal: -583.33 kJ/\$[/tex]
5. Kerosene: -616.67 kJ/\[tex]$
6. Natural Gas: -833.33 kJ/\$[/tex]
Thus, the fuels in the correct order of increasing heat per dollar are:
wood < coal < gasoline < charcoal < kerosene < natural gas
Comparing this with the given options:
1. natural gas < kerosene < wood (incorrect)
2. kerosene < coal < wood (incorrect)
3. wood < coal < natural gas (incorrect)
4. coal < wood < charcoal (incorrect)
5. wood < kerosene < gasoline (incorrect)
None of the given options match the correct order of increasing heat per dollar.
