1.11 Fundamental Quantities and Units Scientists and engineers know that the terms they use, the quantities they measure must all be defined precisely. Such precise and standard measurements can be specified only if there is common system of indication of such measurements. This common system of unit is called 'SI' system i.e. International System of Units. The SI system is divided into six base units and two supplementary units. The six fundamental or base units are length, mass, time, electric current, temperature, amount of substance and luminous intensity, see table 1.4. The two supplementary units are plane angle and solid angle. All other units are derived which are obtained from the above two classes of units. The derived units are classified into three main groups.

1. Mechanical units, 2. Electrical units, 3. Heat units

TABLE 1.4 the six basic SI units.

Quantity Basic unit Symbol Length meter m Mass kilogram kg Time second s Electric current ampere A Thermodynamic temperature kelvin K Luminous intensity candela cd

1.11.1 Multiples and sub-multiples One great advantage of the SI unit is that it uses prefixes based on the power of 10 to relate larger and smaller units to the basic unit. Table 1.5 shows the SI prefixes and their symbols. For example, the following are expressions of the same distance in meters (m): 600,000,000 mm = 600,000 m = 600 km.

TABLE 1.5 the SI prefixes. Multiplier Prefix Symbol 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k

102 hecto h 10 deka da 10−1 deci d 10−2 centi c 10−3 milli m 10−6 micro μ 10−9 nano n 10−12 pico p 10−15 femto f 10−18 atto a

1.11.2 Mechanical Units The various mechanical units are, 1. Mass: It is the matter possessed by the body. It is measured in kg and denoted as m. 2. Velocity: It is the distance travelled per unit time, measured in m/ s and denoted as v. 3. Acceleration: It is the rate of change of velocity measured in m/s2 and denoted as a. 4. Force: It is the push or pulls which changes or tends to change the state of rest or uniform motion of body, measured in Newton (N). One Newton is the force required to give an acceleration of l m/ s2 to a mass of 1 kg. F= m× a N 5. Weight: The gravitational force exerted by the earth on a body is called its weight, measured in Newtons. Weight=m× g where g= gravitational acceleration = 9.81 m/s2

6. Torque: It is the product of a force and a perpendicular distance from the line or action of force to the axis of rotation. It is measured in N-m. T = F × r Where r =radial distance of rotation 7. Work: The work is said to be d one when force acting on a body causes it to move. If a body moves through distance d under the force F then. W = F × d the work is measured in Joules. 8. Energy: It is the capacity to do the work. The work is done always at the cost of energy. The unit of energy is also Joules. The two forms of energy are, i) Kinetic energy: which is the energy possessed by a body due to its motion. If body of mass m is moving with velocity v then the kinetic energy is, K.E. = 1/2 (m v2) J ii) Potential energy: which is the energy possessed by a body due to its position. When a body of mass m is lifted vertically through height of h then the potential energy is, P.E. = m×g×h = W× h J where W =weight

9. Power: The rate of doing work is power measured in J/sec i.e. watts P = work done/ time W And 1 W = 1 J/sec For American automobiles, engine power is rated in a unit called "horsepower," then 1 Horsepower = 745.7 Watts Energy expended = Power× time =work done

1.11.2.1 Relation between Torque and Power Consider a pulley o f radius R and F is the force applied as shown in the Fig. 1.13. T = F × R N-m

Figure 1.13

Let speed of pulley is N revolution per minute. Now work done in one revolution is force into distance travelled in one revolution. d = distance travelled in 1 revolution = 2πR W = work d one in 1 revolution = F × d = 2π R F J The time required for a revolution can be obtained from speed N r.p.m. t = time for a revolution = 60/N sec 푾 ퟐ흅푹푭 ퟐ흅푵 푷 = 풑풐풘풆풓 = = = ( ) ×(푭×푹) 풕 ퟔퟎ ퟔퟎ 푵 P=T × ω Where T = F x R torque in N-m ω= (2πN) / 60 angular velocity in rad/sec The relation P = T ω is very important in analyzing various mechanical system,

1.11.3 Electrical Units The various electrical units are, 1. Electrical work: In an electric circuit, movement of electrons i.e. transfers of charge is an electric current. The electrical work is done when there is a transfer of charge. The unit of such work is Joule. So if V is potential difference in volts and Q is charge in coulombs then we can write, Electrical work = W =V × Q J But I= Q/t,

W =V.I.t J where t = time in second 2. Electrical power: The rate at which electrical work is done in an electric circuit is called an electrical power. Electrical power = P = electrical work / time = W / t = V.I.t / t P=V.I J/sec i.e. watts Thus power consumed in an electric circuit is 1 wall if the potential difference of 1 volt applied across the circuit causes 1 ampere current to flow through it. 3. Electrical energy: An electrical energy is the total amount of electrical work done in an electric circuit. Electrical energy = E = Power × Time = V.I.t joules The unit of energy is joule or watt-sec. As watt-sec unit is very small, the electrical energy is measured in bigger units as watt-hour (Wh) and kilo watt-hour (kWh). When a power of 1 kW is utilized for 1 hour, the energy consumed is said to be 1 kWh. This unit is called a Unit.

1.11.4 Thermal Units

1. Heat energy: The flow of current through a material produces heat. According to the principle of conservation of energy, the electrical energy spent must be equal to the heat energy produced. This is called Joule's law. According to Ohm's law (will see in ch.2) V= IR or I= V/R Heat energy = H = V.I.t = I2Rt = V2t/R joules 2. Specific heat capacity: The quantity of heat required to change the temperature or 1 kilogram of substance through 1 degree Kelvin is called specific heat of the substance.

3. Sensible heat: The quantity of heat gained or lost when change in temperature occurs is called sensible heat. this can be calculated as. Sensible heat = mCΔt Joules. m= Mass of substance in kg C= Specific heat in J/ kg -Ko Δt = change in temperature 4. Latent heat: The quantity of heat required to change the ,ta n- of the substance i.e. solid to liquid to gas with out change in its temperature is called latent heat . It can be calculated as, Latent Heat = m× L joules M= Mass of substance in kg L = Specific Latent heat or specific enthalpy The unit of L is J/kg while unit of latent heat is joules. Total heat= sensible heat + Latent heat The various relations between electrical and thermal units are, 1 calorie= 4.186 joules 1 Joule = 0.2389 calorie 1 kWh= 3.6 ×106 J = 860 kcal 5. Specific enthalpy: It is the heat required to change the state of one kilogram mass of a substance without change in temperature, its unit is J/ kg. 6. Calorific value: Heat energy can be produced by burning the fuels. The calorific value of a fuel is defined as the amount of heat produced by completely burning unit mass of that fuel; it is measured in kJ/gram, kJ/kg. Heat produced in joule= Mass in kg × calorific value in J/kg

1.11.5 Efficiency

The efficiency can be defined the ratio of energy output to energy input. It can be also expressed as ratio of power output to power input. Its value is always less than 1. Higher its value, more efficient is the system of equipment. Generally it is expressed in percentage, its symbol η.

% η = Energy output/ Energy input ×100 = Power output/ power input × 100