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Density and Specific Gravity

Table of Contents
Introduction
Problems
Answers

      
Introduction

                             mass          m
density  =    =  -----------  =  ----
                            volume       V

   
The density is independent of size for any object of uniform composition.

The SI unit for density is kg/m3.  Sometimes units are give in g/ml which is also equal to g/cm3.  

1kg/m3  =  1000 g/  ( 100 cm )3  =  10 -3 g/cm3    thus  3420 kg/m3  =  3.42 g/cm3 

The density is temperature dependent.  Physics Charts - Densities of Substances

Specific gravity is the ratio of the density of the substance to the density of water at 4oC.  Since water is 1.00 g/cm3 or 1.00 x 103 kg/m3, the specific gravity is equal to its density in g/cm3.

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Problems

1.     The approximate volume of the granite monolith known as El Capitan in Yosemite National Park is 10 8 m3.  What is the approximate mass?      Physics Charts - Densities of Substances
    
2. If you tried to nonchalantly smuggle gold bricks by filling your backpack, whose dimensions are 70. cm x 30. cm x 20. cm, what would its mass be?      Physics Charts - Densities of Substances
   
3. A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water.  When filled with another fluid, the mass is 88.78 g.  What is the specific gravity of the second fluid?      Physics Charts - Densities of Substances
   
4. If 5.0 L of antifreeze solution (specific gravity = 0.80) is added to 4.0 L of water to make a 9.0 L mixture, what is the specific gravity of the mixture?

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Answers

1.     The approximate volume of the granite monolith known as El Capitan in Yosemite National Park is 10 8 m3.  What is the approximate mass?      Physics Charts - Densities of Substances
    
  
        m
= ----         Solve for mass and substitute.
        V
    

m  =    V  =  2.7 x 10 3 kg/m3  x  108 m3  =  2.7 x 10 11 kg
   
2. If you tried to nonchalantly smuggle gold bricks by filling your backpack, whose dimensions are 70. cm x 30. cm x 20. cm, what would its mass be?      Physics Charts - Densities of Substances
   
    
V  =  0.70 m  x  0.30 m  x 0.20 m  =  0.012 m 3 

        m
= ----         Solve for mass and substitute.
        V
    

m  =    V  =  19.3 x 10 3 kg/m3  x  0.012  m3  =  230 kg
   
3. A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water.  When filled with another fluid, the mass is 88.78 g.  What is the specific gravity of the second fluid?      Physics Charts - Densities of Substances
   
   
m water  =  98.44 g  -  35.00 g  =  53.44 g

m liquid  =  88.78 g  -  35.00 g  =  43.78 g

Because the volume is the same

   
                                         m liquid         43.78 g
specific gravity liquid  =  -----------  =  ------------  =  0.8192
                                         m water         53.44 g
     
4. If 5.0 L of antifreeze solution (specific gravity = 0.80) is added to 4.0 L of water to make a 9.0 L mixture, what is the specific gravity of the mixture?
   
                 
                                            V water specific gravity water  +  V antifreeze specific gravity antifreeze 
specific gravity mixture  =  ------------------------------------------------------------------------------------------
                                                                                  V mixture  
    

                                             4.0 L x 1.00  +  5.0 L x 0.80
specific gravity mixture  =  ---------------------------------------   =  0.89
                                                               9.0 L
   

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