Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

BUILDING MATERIALS

10.10.2013

DENSITY, POROSITY

DENSITY, POROSITY

PHYSICAL PROPERTIES

PHYSICAL PROPERTIES

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

DENSITY (REAL DENSITY) (NET DENSITY)

ρ

= m

d

/ V

without pores

[kg/m

3

, g/cm

3

]

APPARENT DENSITY

It is defined as the ratio of the mass of a dry material (body)
(m

d

) to its volume without pores (the volume of the solid

matter /skeleton/) (V

without pores

).

It is defined as the ratio of the mass of a dry material (body)
(m

d

) to its total volume (in its natural state) (with pores)

(V

with pores

).

ρ

0

= m

d

/ V

with pores

= m

d

/ V

0

[kg/m

3

, g/cm

3

]

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

DENSITY INDEX

s

= (V

without pores

/ V

with pores

) 100%

POROSITY

It is defined as the ratio (as a percentage) of the volume of
the solid matter /skeleton/ (V

without pores

) to the volume of a

material (body) (V

with pores

).

It is defined as the ratio (as a percentage) of the volume of
pores (V

pores

) to the volume of a material (body) (V

with pores

).

p

= (V

pores

/ V

with pores

) 100%

s = (ρ

0

/ ρ) 100%

p = [1- (ρ

0

/ ρ)] 100%

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

- Crush the sample in a brass (porcelain) (agate) mortar.

- Grind the sample into fine powder in a mill (the complete
elimination of porosity in the solid matter).
- Sieve the sample through 0.08 mm squared meshes.
- Pour the sample into an evaporating dish.
- Dry the sample in a drier in the temperature of 105ºC
(until the mass is constant).
- Cool the sample down to the ambient/room temperature
in the exsiccator (desiccator) (with the hygroscopic
substance at the bottom – e.g. calcium chloride).

DETERMINATION OF DENSITY

PREPARATION OF A

POWDERED MATERIAL

(WITHOUT PORES)

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

- Rinse the Le Chatelier’ flask (cleaned and dried)

with denatured alcohol.
- Fill the flask (volumenometer) with denatured
alcohol to the zero level (‘0 cm

3

’ level = the

bottom of concave meniscus).
- Take out the evaporating dish with the powdered
material /dry/ (the sample) from the exsiccator.

DETERMINATION OF (REAL) (NET)

DENSITY

LE CHATELIER

FLASK (VOLUMENOMETER)

METHOD

APPROXIMATE METHOD

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

- Weigh the evaporating dish with the whole amount of

powdered material (

m

1

).

- Pour the powdered material into the flask (portion by
portion) (without the deposition of the powder on the
interior walls of the flask) to the level of 20 cm

3

(

V

= 20 cm

3

).

- Weigh the evaporating dish with the remained amount of
powdered material (

m

2

).

- Calculate the density of the tested material (

ρ

).

EVAPORATING

DISH

ρ

= (m

1

- m

2

)/ V

V – the volume of the powdered material
poured into the flask (20 cm

3

)

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

- Weigh the empty pycnometer in its dry state (

m

p

).

- Fill about 1/3 of the pycnometer volume with the dry
powdered material (the sample) (stored in the exsiccator).
- Weigh the pycnometer with the sample (

m

p+m

).

- Add distilled water (at the temperature of 20 ºC) to fill up
the volume of pycnometer.

DETERMINATION OF (REAL) (NET)

DENSITY

PYCNOMETER

METHOD

PRECISE METHOD

Every

mass

with the accuracy of 0.001 g!

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

- Weigh the pycnometer with the sample and distilled

water (

m

p+m+w

) (after removing the air bubble).

- Empty the pycnometer and fill it with distilled water.
- Weigh the pycnometer with distilled water (

m

p+w

).

- Calculate the density of the tested material (

ρ

).

V

= m

w

/ ρ

H2O

m

m

= m

p+m

- m

p

m

w

= m

m

+ m

p+m

– m

p+m+w

(the volume of water =

the volume of the powdered material /sample/)

ρ

H2O

= 0.998 g/cm

3

(at the temperature of 20 ºC)

ρ

= m

m

/ V

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

- Dry the sample in the temperature of 105ºC (until the mass

is constant).
- Weigh the dry sample (with the accuracy of 1 g) (

m

d

).

DETERMINATION OF

APPARENT (BULK) DENSITY

DIRECT METHOD

FOR REGULARLY - SHAPED SAMPLES

(e.g. CUBICAL, CUBOIDAL, CYLINDRICAL, CONICAL, SPHERICAL)

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

- Measure all dimensions of the sample (e.g. length /

a

/,

width /

b

/, height /

h

/ for a cuboid) with a slide calliper

(with the accuracy of 1 mm).

DETERMINATION OF APPARENT DENSITY

- Calculate the volume of the sample (

V

0

) (which is equal

to

a x b x h

for a cuboid) and the apparent density (

ρ

0

).

SLIDE
CALLIPER

ρ

0

= m

d

/V

0

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

- Dry the sample in the temperature of 105ºC (until the mass

is constant).
- Weigh the dry sample (

m

d

).

DETERMINATION OF

APPARENT (BULK) DENSITY

INDIRECT METHODS

FOR IRREGULARLY – SHAPED

SAMPLES

1. PARAFFIN WAX METHOD

Materials with large, open pores

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

- Immerse the sample into the melted paraffin wax in

order to achieve a thin coat on its outer surface, as
well as to close all its pores.
- After hardening the wax, weigh the sample with the
paraffin wax cover (

m

sample + wax

).

- Insert the sample with the paraffin wax cover into a

graduated

vessel (beaker) filled with water and note

down its volume (

V

sample + wax

).

PARAFFIN WAX METHOD

V

sample + wax

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

- Calculate the volume of paraffin wax (on the surface of

sample tested) (

V

wax

). The density of parrafin wax equals

0.93 g/cm

3

.

PARAFFIN WAX

METHOD

V

wax

= (m

sample + wax

– m

d

)/ ρ

wax

ρ

wax

= 0.93 g/cm

3

- Calculate the apparent density of the irregularly-shaped

sample (

ρ

0

).

ρ

0

= m

d

/ (V

sample + wax

– V

wax

)

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

ARCHIMEDES’

PRINCIPLE

2. HYDROSTATIC (UNDERWATER) WEIGHING METHOD

(BASED ON ARCHIMEDES’ PRINCIPLE)

The

buoyant force

, acting on a submerged object (body),

is equal to the weight of water (liquid) displaced by the
object (body). The force is directed upwards.

G – weight in the air
(gravity force)

R – weight in water
(resultant force)

B – buoyancy
(buoyant force)

B

G

G

R

G

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

HYDROSTATIC WEIGHING

METHOD

B

G

G

g

ρ

V

=

g

ρ

V

=

g

m

=

B

0

2

H

0

2

H

displaced

water

displaced

water

g

m

=

G

a

g

m

=

R

w

B

–

G

=

R

R

G

B

g

ρ

V

–

g

m

=

g

m

0

2

H

a

w

0

2

H

w

a

ρ

/

)

m

–

m

(

=

V

ρ

H2O

– density of water, ρ

H2O

= 1 g/cm

3

g – gravitational acceleration (acceleration due to gravity)

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

HYDROSTATIC WEIGHING METHOD

- Dry the sample in the temperature of 105ºC (until the mass

is constant).
- Weigh the dry sample (

m

d

).

- Put the dry sample in water and saturate it (until the mass
is constant = all pores are filled with water).
- Weigh the saturated sample in the air (

m

a

).

- Weigh the saturated sample in water (

m

w

).

- Calculate the volume of the irregularly-shaped sample (

V

).

- Work out the apparent density of the irregularly-shaped
sample (

ρ

0

).

ρ

0

= m

d

/ V

V = (m

a

– m

w

)/ ρ

H2O

Project “The development of the didactic potential of Cracow

University of Technology in the range of modern construction”

is co-financed by t he European Union

within the confines of the European Social Fund and realized under surveillance of Ministry of Sci ence and Higher Education

Sources of the figures (images):

http://www.thesciencefair.com
http://etc.usf.edu/clipart/26800/26841/pycnometer_26841.htm
http://etc.usf.edu/clipart/26800/26842/pycnometer_26842.htm
http://renelleesa.blogspot.com/2010/10/difference-between-cube-and-

cuboid.html

http://www.tutorials.com/04/0481/048112.asp
http://www.clker.com/clipart-14830.html
http://homepage.smc.edu/walker_muriel/measurements_in_the_laboratory%20

Procedure.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy4.html
http://schools.wikia.com/wiki/Buoyancy_&_Archimedes’_Principle