Temperature and Density

Density Math

Recall: Density is defined by a simple equation , which has three related forms:

If you have problems with cross multiplication , remember that ‘pyramids’ can also be used to solve density and other 3 variable equations :

Example: 23.5 mL of a certain liquid weighs 35.062 g. What is the density
of the liquid? What mass will 20mL of this liquid have?

Density Applications

Finding the Volume and / or Density of Solid Objects

Irregular shaped objects

Any Object will DISPLACE it’s own volume of water when submerged

Recall lab: Sketch the apparatus you used to measure the volume of
the rubber stopper:

Example: A solid object weighing 15.250 g is submerged in water, during
which time the water level rose from 50.0 mL to 60.2 mL. What is the
density of the object?

Regular shaped objects

Regularly shaped objects ( cubes , ‘bricks’, spheres, cylinders, c ones ….) have equations that define their volume.

Task: Sketch the following 3-D shapes and list the equations that define their volume (see
your text book)

1. Find the volume of the object in question via the equation that defines its volume (be sure to use cm for all length dimensions). 2. Substitute the derived volume value in D = M/V to find the object’s density (recall that mass is measured in grams).

Recall: the radius of a circle equals half of it’s diameter (i.e. dia.= 2r)

Example: Dice used in Las Vegas weigh 2.65 g and have sides of length 1.2 cm. What is the density of a Las Vegas dice?

Densities of common materials

Material	State (s), (l) or (g)	Density (g/cm3)
Oxygen		0.00133
Ethanol		0.785
Water		1.000
Iron		7.87
Silver		10.5
Lead		11.34
Mercury		13.6
Gold		19.32

“Will it Float?”

The David Let terman Show on CBS often features a segment called ‘Will it Float’. Simply, Dave and Paul try to determine if an object, such as a refrigerator or 100 ft of insulation cable, will float when dropped into a large container of water.

Question: What physical property of a material will determine ‘if it will
float’? What would be a more scientifically accurate (if less catchy) name
for the ‘Will it float’ segment on Dave’s show?

	Discussion: “Battleships and dating advice”

Task: Using the table supplied above, sketch a picture of what would happen
if ~30 mL samples of ethanol, mercury and water, as well a silver dollar and
a gold ring were added to a volumetric cylinder.

Question of the week ( group work )

If a 200 mg piece of gold is hammered into a sheet measuring 2.4 ft by 1.0
ft, then what is the sheet’s thickness in meters? If a gold atom is 0.26 nm
wide, how many atoms thick is the sheet?

“The Wire” & “Sketch” The following questions were taken from your 1st practice midterm:

A copper (Cu) wire has a mass of 4.00 pounds and a diameter of 5.00 mm. Determine
the wire’s mass and in the units specified below. Include any appropriate decimal
prefixes in your final answers. Density °F copper = 8.95 g/cm³

Mass of the wire in kg:

ANS: 1.81 kg (3 sf)

Volume of the wire in cm³:

ANS: 202 mL (3 sf)

Sketch a fully labeled diagram illustrating the appearance of a 100 mL cylinder after the
following items have been added to it: