COMMON SYSTEMS OF MEASUREMENTS

Transcription

1 31 SI Units CHAPTER CONTENTS COMMON SYSTEMS OF MEASUREMENTS (1) Metric Syste (2) SI Syste SI UNIT OF LENGTH SI UNIT OF VOLUME SI UNIT OF TEMPERATURE UNITS OF MASS AND WEIGHT UNITS OF FORCE UNITS OF WORK AND HEAT ENERGY UNITS OF PRESSURE UNIT OF DENSITY COMMON SYSTEMS OF MEASUREMENTS There are two coon systes of easureent. (1) Metric Syste This is a decial syste of weights and easures originally based on the eter as the unit of length and the kilogra as the unit of ass. (2) SI Syste The International syste of units was adopted by the 11th General Conference of Weights and Measures in The SI units are widely used but they have not been fully accepted by the scientific counity. In fact, etric syste is still used in ost countries. The Aerican textbooks ake use of the etric syste freely. May be that Aerica reverts to the etric syste over the years. In this book we have used the etric units throughout. However, at several places the SI units have also been used as we feel that in the present state of confusion the student should be conversant with both types of units. Here, we will discuss the etric and the SI units as also the conversion factors. 1063

2 PHYSICAL CHEMISTRY TABLE SI BASE UNITS Physical Quantity Unit Sybol Length eter Mass kilogra kg Tie second s Teperature kelvin K Electric current apere A Nuber of particles ole ol SI UNITS OF LENGTH The SI unit of length is the eter (). Fractions and ultiples of SI units are naed by adding appropriate prefixes. The coonly used etric length units are listed in Table TABLE COMMON METRIC LENGTH UNITS Unit Sybol Relation eter kiloeter k 1 k = 10 3 decieter d 1 d = 10 1 centieter c 1 c = 10 2 illieter 1 = 10 3 icroeter 1 μ = 10 6 nanoeter n 1 n = 10 9 picoeter p 1 p = angstro Å 1Å = 10 8 c = Even though the unit angstro (Å) is not part of the SI syste, it is still used for distances between atos. Currently, the interatoic distances are soeties reported in units of nanoeters (n) or picoeter (p). 1 n = 10 Å 1 p = 10 2 Å 1 n = 10 3 p It ay be noted that the etric sybols are not changed into plurals. Thus five centieters of length is written as Correct Incorrect 5 c 5 c. 5 c.. 5 cs SI UNITS OF VOLUME The derived SI unit of volue is Cubic eter 3 This is the volue of a cube that is 1 eter on each edge. The related units of volue which are also used are : Cubic centieter c 3 Cubic decieter d 3

3 SI UNITS c 3 = 1 L 1 d 3 = 1000 c 3 = 1 L 1000 l = 1 L c 20 c 20 c 10 c 10 c 20 c Figure 31.1 Relationship between length and volue. Another coon easure of volue is the litre (a non-si unit) which is denoted by L ( or l). A liter is the volue occupied by a cube 10 c on edge. That is, Also 1 L = (10 c) 3 = 1000 c 3 1 L = 1000 L Therefore 1000 L = 1000 c 3 1 L = 1 c 3 (cc) Hence the volue units illilitre (L) and cubic centieter (cc) can be used interchangeably. It ay again be stated that etric sybols are not changed into plurals. Thus, Correct L (or l) Incorrect Ls (ls),.l., l. SI UNIT OF TEMPERATURE The series of arkings on a theroeter which read teperature is called a teperature scale. A teperature scale in which 0º is assigned to the freezing point of pure water and 100º to the boiling-point is known as the Celsius scale. The teperatures are expressed in degrees Celsius (ºC). Roo teperature on the celsius scale is taken to be 25 C. The celsius scale is not a part of the SI syste. Since it is widely used in scientific literature, it is difficult to abandon it. The SI syste uses the Kelvin scale. A degree on the Kelvin scale has the sae agnitude as a degree on the celsius scale but zero on the Kelvin scale equals ºC. Thus the teperature (0 K) is often referred to as the absolute zero. Celsius and Kelvin teperature are related as K = C , C = K It ay be noted that the unit for teperature on the Kelvin scale is K and not K. This notation has been approved by IUPAC and is now used by cheists all over the world. Thus it ay be noted that a degree sign ( ) is not used with the Kelvin scale.

4 PHYSICAL CHEMISTRY On the Fahrenheit scale pure water freezes at 32º and boils at 212º. Thus 100º celsius equals = 180 Fahrenheit degrees. Celsius and Kelvin teperatures are related by the following equations. 5 ºC = ( ºF 32) 9 9 ºF = ºC Using these relations it is easy to convert a teperature reading fro Fahrenheit to Celsius and vice versa. Kelvin Celsius Fahrenheit Boiling point of water Noral body teperature Average roo teperature Freezing point of water Sae reading on Fahrenheit and Celsius scales Figure 31.2 A coparison of Kelvin, Celsius, and Fahrenheit scales. UNITS OF MASS AND WEIGHT A beginner is apt to confuse ass with weight. The two quantities are related but are not equal. The ass () of an object is the aount of atter contained in that object. Mass is an invariant property of an object. It is the sae on the surface of the earth as on the surface of the oon. The weight (w), on the other hand, is force and not ass. It can be calculated by ultiplying ass with the gravitational acceleration (g). That is, w = g The gravitational pull on an object decreases as the object is oved farther fro the centre of the earth. Thus astronauts lose weight as they ove higher and higher fro earth. It follows, therefore, that even though the weight of an object can vary at different places, its ass stays the sae. Although ass and weight are not the sae, the two ters are used interchangeably even by the scientific counity. This is so because an object of a certain ass weigh with virtually the sae anywhere on the earth. Known asses, for exaple, are easured by a process tered weighing with a balance. The basic unit of ass in the etric syste (or SI syste) is gra. The coonly used units based on the gra are listed in Table 31.3.

5 SI UNITS 1067 TABLE COMMONLY USED METRIC WEIGHT AND MASS UNITS Unit Sybol In ters of gras gra g Kilogra kg 1 kg = 10 3 g illigra g 1 g = 10 3 g icrogra μg 1 μg = 10 6 g The British syste of etric weights is also used by cheists in which ounce (1 1b = 16 oz) 1 lb = g pound 1 lb lb = 1kg ton (1 ton = 2000 lb) It ay be noted that etric units are not pluralised. Thus, Correct Incorrect 2 g 2gs, 2gs, 2g.. UNITS OF FORCE Force (F) is defined as the product of ass () and acceleration (a). F= a Acceleration is the change in velocity (v) per unit tie (t). Velocity is the change in distance (l) per unit tie. Using SI base units, we can derive the unit for acceleration. UNIT distance l distance velocity tie change in velocity acceleration. a 2 tie s The derived SI unit for force, then, is kg s 2. The unit is called newton and has the sybol N. Thus, 1 N = 1 kg s 2 UNITS OF WORK AND HEAT ENERGY Work has been defined as the product of the force and the distance through which it operates w = f d Because force is expressed in newtons and distance in eters, the SI units of work and energy is the newton-eter. It is also called Joule (J). 1J = 1 N Heat is energy that flows fro one object to another because of a teperature difference between the objects. The quantity of heat transferred is best expressed in joules. But it is often given in calories (cal). One calorie is defined as exactly joules. Thus, 1 cal = J v s

6 PHYSICAL CHEMISTRY One calorie of energy will raise the teperature of 1 g of liquid water by 1 C. The calorie is a non-si unit, but like the joule it can be used for any for of energy. The calorie written with a capital C is equal to one kilocalorie, 1000 calories. Thus, 1 C = 1000 cal UNITS OF PRESSURE Pressure is defined as the force per unit area exerted on a surface. That is, F P = A Thus we can deterine the SI unit for pressure as : UNIT Force F kg s 2 or N Area A 2 Pressure P kg 1 s 2 or N 2 A The SI unit N 2 is naed pascal and given the sybol Pa. Three other units which have been traditionally used are : atosphere, sybol at, is defined as the pressure exerted by a colun of ercury 760 in height at 0ºC. torr, sybol Torr, is defined as the pressure exerted by a 1 colun of ercury at 0ºC. illieter of ercury or Hg, which is the height in illieters of ercury that the pressure can support. The various units of pressure are related as 1 at = 760 Torr = 76 Hg = Pa The three non-si units viz., Torr and Hg are still coonly used in current practice and it will take quite soe tie before the scientific counity adopts the SI unit Pa. UNITS OF DENSITY One of the physical properties of a solid, a liquid, or a gas is its density (d). Density is defined as ass per unit volue. This ay be expressed atheatically as d = V By using the base SI units and reebering that the unit for volue is 3, we can derive the SI unit for density. kg 3 3 or kg The other units of density coonly used are g c 3 or g l 1 for liquid or solid densities g L 1 or g d 3 for gas densities The ter specific gravity is the ratio of the density of a substance to the density of a reference substance. The reference substance for solids and liquids is usually water. density of a substance sp gr = density of reference substance Specific gravity, being the ratio of two densities has no units.