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Question: An empty density bottle of weight \[30g\], when filled completely with water weighs \[62g\]. When fi...

An empty density bottle of weight 30g30g, when filled completely with water weighs 62g62g. When filled completely with another liquid the weight is 54g54g
Calculate -
(a) The volume of density bottle
(b) The density of the liquid

Explanation

Solution

Here mass of bottle, mass of bottle when completely filled with water and another liquid are given. From these values we can find out the individual mass of water as well as liquid. Here the volume of water and liquid will be equal to the volume of the bottle. We know that density is mass per volume. Using this formula, we can calculate the density of the liquid.
Formula used:
Density of the liquid=Mass of liquidvolume of liquid\text{Density of the liquid=}\dfrac{\text{Mass of liquid}}{\text{volume of liquid}}

Complete step by step answer:
Given,
Mass of empty density bottle, m1=30g{{m}_{1}}=30g
mass of density bottle and water, m2=62g{{m}_{2}}=62g
Mass if density bottle and liquid, m3=54g{{m}_{3}}=54g
Mass of water =m2−m1=62−30=32g={{m}_{2}}-{{m}_{1}}=62-30=32g

a) Volume of 1 g of water=1cm3=1c{{m}^{3}}
Here, the density bottle is completely filled with water. Then,
Volume of density bottle = volume of 32 g of water =32cm3=32c{{m}^{3}}

b) Mass of liquid, m4=m3−m1=54−30=24g{{m}_{4}}={{m}_{3}}-{{m}_{1}}=54-30=24g
Volume of 24g24gof liquid= Volume of density bottle =32cm3=32c{{m}^{3}}
Then,
Density of the liquid=Mass of liquidvolume of liquid=2432=0.75g/cm3\text{Density of the liquid=}\dfrac{\text{Mass of liquid}}{\text{volume of liquid}}=\dfrac{24}{32}=0.75g/c{{m}^{3}}

Note:
Mass per unit volume is defined as the density of a material. A density bottle can be used to determine the density of liquid. A density bottle is a glass bottle with a circular glass stopper at its neck which has a fine hole in it. Different materials have different densities. Hence, density is often used as a method to identify a substance.

Note:
Comparing the densities of two substances can also predict how substances interact with each other. Water is used as the common standard to the materials and it has a density of 1000 kg/m3 1000\text{ }kg/{{m}^{3~}} at Standard Temperature and Pressure. But water’s density will change based on the temperature even if the pressure is consistent.