Unit Systems and Dimensional Analysis PDF

Unit Systems and Dimensional Analysis Metric system of units (Length, Mass, and Volume) Units in mathematical operations Conversion factors Dimensional analysis Density Temperature units Units in Measurements: Unit = a label for the property being measured. A measurement must have a un...

Unit Systems and Dimensional Analysis Metric system of units (Length, Mass, and Volume) Units in mathematical operations Conversion factors Dimensional analysis Density Temperature units Units in Measurements: Unit = a label for the property being measured. A measurement must have a unit. Units are very case sensitive. g G m M Systems of Units: – Metric System – English System Metric System A prefix can be attached to a base unit of the property being measured. Each prefix increases or decreases the size of the base unit by some factor of 10. The prefixes are written before the base unit of the property. Ex: base unit for weight/mass is g (grams). Other metric units for the same property can be Tg, kg, cg, mg, ng, etc. Prefix Symbol Numerical Value mega M 1,000,000 (106) kilo k 1,000 (103) BASE UNIT 1 centi c 0.01 (10-2) milli m 0.001 (10-3) micro m 0.000001 (10-6) nano n 0.000000001 (10-9) To Use the Metric System When determining the relationship between two metric units of the same property: Ex: kg = ? g Write a value of 1 for the prefixed unit and then write the 10x value of that prefix for the base unit. 1 kg = 103 g mol = ? mmol nm = ? m Length: Distance between two points Base unit in metric system = m (meters) m = ? km cm = ? m mm = ?m Units of length in English system: in ( 1 in = 2.54 cm) ft ( 1 ft = 12 in) yards ( 1 yd = 3 ft) mi ( 1 mi = 5280 ft) ( 1 mi = 1.609 km) Mass: amount of matter in a substance Base unit in metric system = g (grams) g = ? cm mg = ? m g = ?kg Units of mass in English system: oz ( 1 lb = 16 oz) lb ( 1 lb = 453.6 g) ( 1 ton = 2000 lb) Volume: space occupied by a substance Base unit in metric system = L (Liters) L = ? mL 1 L is defined as the area of a cube of dimensions 10 cm.  V = 10cm x 10 cm x 10 cm = ?  1 mL = 1cm3 Units of Volume in English system: qt ( 1 gal = 4 qt) gallon ( 1 gal = 3.785 L) Time Base unit in metric system = s (seconds) s = min min = hr  Temperature: measure of hotness/coldness of a substance Metric units = oC (degree celcius/Centigrade) K (kelvin) K = oC + 273 o C = K - 273 English unit = oF (degree farenheit) o F = (1.8 oC) + 32 o C = (oF – 32) 1.8 Units in Mathematical Operations g x g x cm = g2cm nm = nm/hr hr mol x L = mol.L/mi mi