An empty relative density bottle weigh 15g.It weighs 165kg when filled with a liquid and 175g when filled with water. Calculate the density of the liquid.
To calculate the density of the liquid, we need to first understand what relative density is. Relative density, also known as specific gravity, is the ratio of the density of a substance to the density of a reference substance. In this case, the reference substance is water.
Let's break down the information given:
- An empty relative density bottle weighs 15g.
- When filled with the liquid, it weighs 165kg.
- When filled with water, it weighs 175g.
Step 1: Calculate the mass of the liquid:
The difference between the weight of the bottle when filled with the liquid and when empty will give us the weight of the liquid:
Mass of the liquid = Weight of the bottle filled with the liquid - Weight of the empty bottle
= 165g - 15g
= 150g
Step 2: Calculate the density of the liquid:
Density is defined as the mass per unit volume. We can use the formula:
Density = Mass / Volume
In this case, we know the mass of the liquid (150g), so we need to determine the volume.
To find the volume of the liquid, we need to compare it to the volume of water.
Let's use the weight of the liquid and the weight of the water to find their respective volumes.
Step 3: Calculate the volume of the liquid and water.
Given that the weight of the water-filled bottle is 175g, minus the weight of the empty bottle (15g), we can calculate the weight of the water alone:
Weight of the water = Weight of water-filled bottle - Weight of empty bottle
= 175g - 15g
= 160g
Knowing that the density of water is 1g/cm³, we can calculate the volume of water:
Volume of water = Weight of water / Density of water
= 160g / 1g/cm³
= 160 cm³
Similarly, using the weight of the liquid (150g), we can calculate its volume:
Volume of liquid = Weight of liquid / Density of liquid
Step 4: Calculate the density of the liquid:
Now we can substitute the values we have into the density formula to find the density of the liquid:
Density of the liquid = Mass of the liquid / Volume of the liquid
= 150g / Volume of the liquid
Since we don't have the volume of the liquid, we can't calculate the exact density. We would need additional information to complete the calculation.
But based on the given information, we can determine that the density of the liquid is less than 1g/cm³, as the total weight of the filled bottle (165g) is less than the weight of the water (175g), meaning the liquid is less dense than water.