WORK POWER AND ENERGY CH-3

Joule’s Law of Electric Heating

The amount of work required to maintain a current of I amperes through a resistance of R ohm for t second is

W.D. = I² Rt joules

= VIt      joules                                                              ( * R = V/I)

= Wt       joules                                                              ( * W = VI)

= V²t/R joules                                                               ( * I = V/R)

where	J	= 4,186 joules/kcal = 4,200 joules / kcal (approx)
*	H	= I2Rt/4,200 kcal = Vlt/4,200 kcal = Wt/4,200 kcal = V2t/4,200 R kcal

S.I. Units

1.  Mass. It is quantity of matter contained in a body.

Unit of mass is kilogram (kg). Other multiples commonly used are :

  1 quintal = 100 kg, 1 tonne = 10 quintals = 1000 kg

2.       Force. Unit of force is newton (N). Its definition may be obtained from Newton’s Second Law of Motion i.e. F = ma.

If m = 1 kg ; a = 1m/s², then F = 1 newton.

Hence, one newton is that force which can give an acceleration of 1 m/s² to a mass of 1 kg. Gravitational unit of force is kilogram-weight (kg-wt). It may be defined as follows :

or

It is the forcewhich can impartan acceleration of 9.8 m/s² to a mass of 1 kg. It is the force whichcan impart an acceleration of 1 m/s² to a mass of 9.8 kg. Obviously,       1 kg-wt. = 9.8 N  

3.   Weight. It is the force with whichearth pulls a body downwards. Obviously, its unitsare the

same as for force.

(a)     Unit of weight is newton(N)

(b)    Gravitational unit of weight is kg-wt.*

        Note.  If a body has a mass of m kg, then its weight, W = mg newtons = 9.8 newtons.                               

4.  Work, If a force F moves a body through a distance S in its direction of application, then

 Work done W = F ´ S 

(a)    Unit of work is joule (J).

If, in the above equation, F = 1 N : S = 1 m ; then work done = 1 m.N or joule.

Hence, one joule is the work done when a forceof 1 N moves a body througha distance of 1 m in the direction of its application.

(b)   Gravitational unit of work is m-kg. wt or m-kg**.

*      Often it is referred to as a force of 1 kg, the word ‘wt’ being omitted.  To avoid confusion with mass of 1 kg, the force of 1 kg is written in engineering literature as kgf instead of kg. wt.

** Generally the work ‘wt’ is omitted and the unit is simply written as m-kg.

If F = 1 kg-wt; S = 1 m; then W.D. = 1 m-kg. Wt = 1 m-kg.

Hence, one m-kg is the work done by a force of one kg-wt when applied over a distance of one metre.

Obviously, 1 m-kg = 9.8 m-N or J.

5.    Power. It is the rate of doing work. Its units is watt (W) which represents 1 joule per second. 1 W = 1 J/s

If a force of F newton moves a body with a velocity of nm./s then

  power =  F ´ n watt If the velocity n is in km/s, then

 power = F ´ nkilowatt

6.    Kilowatt-hour (kWh) and kilocalorie (kcal)

´

1 kWh  =  1000     1 Js ´ 3600 s = 36 ´10⁵ J

1 kcal = 4,186 J \ 1 kWh = 36 ´ 10⁵/4, 186 = 860 kcal

7.    Miscellaneous Units

(i)    

1 watt hour (Wh) = 1 J ´ 3600 s = 3600 J

(ii)     1 horse power (metric) = 75 m-kg/s = 75 ´ 9.8 = 735.5 J/s or watt

(iii)     1 kilowatt (kW) = 1000 W and 1 megawatt (MW) = 10⁶ W