1
•Derived units (derived from the base units)
–Volume (V)→1 m3= (1 m) ×(1 m) ×(1 m)
1 mL = 1 cm3= (1 cm)×(1 cm)×(1 cm) =
(10-2 m)×(10-2 m)×(10-2 m) = (10-2×10-2×10-2) m3= 10-6 m3
1 L = 1 dm3= 10-3 m31 mL= 10-3 L
–Density (d)→mass (m) per unit volume (V)
→(d= m/V)
unit of d= (1 kg)/(1 m3) = 1 kg/m3
–Velocity (v)→distance (l) per unit time (t)
→(v= l/t)
unit of v= (1 m)/(1 s) = 1 m/s
•Extensive properties – depend on sample
size (mass, volume, length, ...)
•Intensive properties – independent of
sample size (density, temperature, color, ...)
Example:
What is the density of an alloy in g/cm3, if
55 g of it displace 9.1 mL of water?
d= m/V= (55 g)/(9.1 mL) = 6.0 g/mL =
6.0 g/cm3
Example:
• Convert the density of gold, 19.3 g/cm3, to
kg/m3.
⇒need to convert both the numerator and
denominator g→kg and cm3→m3
1 kg = 103g
1 cm = 10-2 m ⇒1 cm3= (10-2)3m3= 10-6 m3
3
3
36
3
33 10319
10
1
10
g 1
319 m
kg
.
m
cm
g
k
cm
g
.d ×=
×
×= −
Example:
What is the mass in kg of a 15 ft wire made of
an alloy with d = 6.0 g/cm3if the diameter of the
wire is 0.20 in?
Plan:
Diameter→radius (cm)→cross-section area (cm2)
Length (cm) ×cross-section area →volume (cm3)
Volume & density →mass (g) →mass (kg)
15 ft
0.20 in
