Measurements and Solving Problems

• 2.1 Units of Measurements The SI Measurement System 1. unit of measurement: physical quantity of

a defined size

2. standard of measurement: objects or natural phenomena of constant

value, easy to preserve and reproduce

Seven Fundamental SI Units 1. Length standard unit is the meter

meter: the distance light travels in a vacuum during a time

interval 2. Mass standard unit is the kilogram

3. Time standard unit for time is the second

4. Temperature based on Kelvin

5. Amount of substance : mole 6. Electric current: ampere 7. Luminous intensity: candela

Prefix Symbol Exponential factorGiga G 109

Mega M 106

Kilo k 103

Hecto h 102

Deca da 101

Deci d 10-1

Centi c 10-2

Milli m 10-3

Micro υ 10-6

Nano n 10-9

Units of measurement in calculations1. Factor-label method A problem solving method based on

using units as algebraic factors.

2. Unit conversion A ratio derived from the equality between

two different units and can be used to convert from one unit to the

other.

3. Examples: a. Convert 75 dollars to quarters 75 dollars x 4 quarters = 1 dollar

b. Convert 92 mg to g

92 mg x 1 g 1000 mg

=

c. Convert 25 cm to m.

d. Convert 72.0 g to micrograms

Derived SI Units1. A unit that can be obtained from combinations

of fundamental units.2. Volume The amount of space occupied by an

object

length x width x height cm x cm x cm = cm3

**** 1 L = 1000 mL = 1000 cm3

3. Density Relates the mass of substance to its

volume, or its mass per unit volume

density = mass volume

or d = m v

units for density: gases: kg m3

solid: g cm3

liquid: g mL

Example: 1. Find the density of a piece of aluminum

with a volume of 4.0 cm3 and a mass of 10.8 g. Is aluminum more dense or less dense than lead? (Dlead = 11.35 g/cm3)

2.2 Heat and Temperature 1. Temperature: is the measure of the

average kinetic energy of the particles in a sample of matter

2. Heat (heat energy): the sum total of the kinetic energies of

the particles in a sample of matter

3. Units of temperature degree Celsius water freezes at 0 °C water boils at 100 °C degree Fahrenheit water freezes at 32 °F water boils at 212 °F Kelvin K = 273 + °C

Temperature conversions: °C = 5/9 x ( °F -32)

°F = 9/5(°C) + 32

4. Units of heat a. joule (J): SI unit of heat

b. calorie: the quantity of heat required to raise the temperature of 1 g of

water 1 °C

**** 1 cal = 4.184 J

c. Ex. Convert 275 cal to joules and kilojoules. 1.

2.

5. Heat capacity and specific heat three things determine heat change 1. the nature of the matter changing

temperature

2. the mass

3. the size of the temperature change

heat capacity: amount of heat energy needed to raise the

temperature of a given sample of matter by one Celsius degree

specific heat: the amount of heat energy required to raise the temperature

of 1 g of a substance by one Celsius degree

• Common specific heats

equation: q = mCΔT

where q = heat (absorbed or released) m = mass C = specific heat ΔT = final temp – initial temp

Example: A 4.0 g sample of glass was heated

from 1 °C to 41 °C, and was found to have a specific heat of 0.20 J/g°C. How much heat was gained?

• 2.3 Using Scientific measurementsAccuracy and precisionAccuracy: refers to the closeness of a

measurement to the true or accepted value of the quantity measured

Precision: refers to the agreement among the numerical values of a set of measurements of the same quantity made in the same way

percent error: % error = accepted value – experimental value x 100 accepted value

Significant figures: See handout Reading scales:1. 2. 3.

• Quantitative Problems 1. How many cm are in 35 inches?

2. How many gallons are in 50 liters?

3. How many km/min is 32 mi/hr?