To find the volume of 2.3 kg of diesel fuel, given its density and the conversion factors, we'll proceed step by step.
1. Convert mass from kilograms to grams:
Since density is given in grams per milliliter, we need to use grams for the mass.
[tex]\[
\text{Mass in grams} = 2.3 \, \text{kg} \times 1000 \, \frac{\text{g}}{\text{kg}} = 2300 \, \text{g}
\][/tex]
2. Calculate the volume in milliliters:
Using the given density of diesel fuel (0.839 g/mL), we can find the volume in milliliters.
[tex]\[
\text{Volume in mL} = \frac{\text{Mass in grams}}{\text{Density}} = \frac{2300 \, \text{g}}{0.839 \, \frac{\text{g}}{\text{mL}}} \approx 2741.36 \, \text{mL}
\][/tex]
3. Convert milliliters to liters:
There are 1000 milliliters in a liter.
[tex]\[
\text{Volume in L} = \frac{\text{Volume in mL}}{1000} = \frac{2741.36 \, \text{mL}}{1000} \approx 2.74 \, \text{L}
\][/tex]
4. Convert liters to gallons:
Given that 1 gallon is 3.79 liters, we can find the volume in gallons.
[tex]\[
\text{Volume in gallons} = \frac{\text{Volume in L}}{3.79 \, \frac{\text{L}}{\text{gallon}}} = \frac{2.74 \, \text{L}}{3.79 \, \frac{\text{L}}{\text{gallon}}} \approx 0.723 \, \text{gallons}
\][/tex]
Thus, the volume of 2.3 kg of diesel fuel is approximately:
- 2741.36 milliliters
- 2.74 liters
- 0.723 gallons
