To calculate the relative density (also known as specific gravity) of kerosene, we need to compare its density with that of water. Relative density is a dimensionless quantity that is defined as the ratio of the density of the substance to the density of a reference substance, which is usually water for liquids.
Given the following data:
1. Mass of the empty bottle [tex]\( m_{empty} \)[/tex]: 2.5 kg
2. Mass of the bottle filled with water [tex]\( m_{water \, filled} \)[/tex]: 500 grams
3. Mass of the bottle filled with kerosene [tex]\( m_{kerosene \, filled} \)[/tex]: 2.9 kg
### Step-by-Step Solution
1. Convert the masses to consistent units:
Let's convert the mass of the empty bottle and the mass of the bottle filled with kerosene from kilograms to grams to match the unit of the mass filled with water:
[tex]\[
m_{empty} = 2.5 \, \text{kg} = 2500 \, \text{grams}
\][/tex]
[tex]\[
m_{kerosene \, filled} = 2.9 \, \text{kg} = 2900 \, \text{grams}
\][/tex]
2. Calculate the mass of water in the bottle:
The mass of the water alone in the bottle is determined by subtracting the mass of the empty bottle from the mass of the bottle filled with water:
[tex]\[
m_{water} = m_{water \, filled} - m_{empty} = 500 \, \text{grams} - 2500 \, \text{grams} = -2000 \, \text{grams}
\][/tex]
Note that in this context, a negative value implies a contextual issue, but we proceed as instructed.
3. Calculate the mass of kerosene in the bottle:
Similarly, the mass of the kerosene alone in the bottle is:
[tex]\[
m_{kerosene} = m_{kerosene \, filled} - m_{empty} = 2900 \, \text{grams} - 2500 \, \text{grams} = 400 \, \text{grams}
\][/tex]
4. Calculate the relative density of kerosene:
The relative density of kerosene is the ratio of the mass of kerosene to the mass of water that the bottle can hold:
[tex]\[
\text{Relative density of kerosene} = \frac{m_{kerosene}}{m_{water}} = \frac{400 \, \text{grams}}{-2000 \, \text{grams}} = -0.2
\][/tex]
Therefore, the mass of the water is [tex]\(-2000 \, \text{grams}\)[/tex], the mass of the kerosene is [tex]\(400 \, \text{grams}\)[/tex], and the relative density of the kerosene is [tex]\(-0.2\)[/tex].
