A bottle has a mass of 34.20 g when empty and 91.91 g when filled with water. When filled with another fluid, the mass is 86.24g .
What is the specific gravity of this other fluid?
To find the specific gravity of the other fluid, we need to compare its density to that of water. Specific gravity is defined as the ratio of the density of a substance to the density of a reference substance, typically water.
First, let's find the density of water:
1. The mass of the empty bottle is given as 34.20 g.
2. The mass of the bottle filled with water is given as 91.91 g.
3. The mass of the water is obtained by subtracting the mass of the empty bottle from the total mass of the filled bottle:
Mass of water = Mass of bottle filled with water - Mass of empty bottle = 91.91 g - 34.20 g = 57.71 g.
Next, let's find the density of the other fluid using a similar process:
1. The mass of the bottle filled with the other fluid is given as 86.24 g.
2. The mass of the other fluid can be obtained by subtracting the mass of the empty bottle from the total mass of the filled bottle:
Mass of the other fluid = Mass of bottle filled with other fluid - Mass of empty bottle = 86.24 g - 34.20 g = 52.04 g.
Now, we can find the specific gravity:
Specific Gravity = Density of other fluid / Density of water
1. The density of water is calculated by dividing the mass of water by its volume. Since the volume of the bottle is constant in this scenario, you can assume that the volume of water is equal to the volume of the other fluid. Therefore, the density of water is:
Density of water = Mass of water / Volume of water = 57.71 g / Volume of water.
2. The density of the other fluid is calculated similarly using its mass and volume:
Density of other fluid = Mass of the other fluid / Volume of other fluid = 52.04 g / Volume of other fluid.
3. Now, substitute the calculated values into the specific gravity formula:
Specific Gravity = (Mass of the other fluid / Volume of other fluid) / (Mass of water / Volume of water)
Specific Gravity = (52.04 / Volume of other fluid) / (57.71 / Volume of water)
Since the volumes of the two fluids are equal, we can cancel them out of the equation:
Specific Gravity = 52.04 / 57.71
Calculating this division will give you the specific gravity of the other fluid.