Question

Define $1J$ of work and $1$ watt of power.

Answer 1

Hint: To solve this question, we have to use the basic definitions of the work done, and the power. From there, we can easily define $1J$ of work and $1$ watt of power.

Complete step-by-step answer:
We know that the work done in mechanics is defined as the dot product of the force and the displacement of a particle. So it is given by
$W = F \cdot S$ …………………….(1)
Whenever work is done on a system, then its energy gets increased or decreased. The energy supplied by the work done on a system may be in any of its forms. It can change its gravitational potential energy, kinetic energy, electrostatic potential energy etc. So we can say that the work done is basically a form of energy.
We know that the standard unit for the energy is accepted to be one Joule in the mks, or the SI system of units.
As we have appreciated above that work done is a form of energy, so the SI unit of work is also one Joule.
From (1) we can say that for having the value of the work done to be equal to one Joule, we need a force of one Newton applied on a particle, which produces a displacement of one meter, in the direction of the force. So one Joule can be defined as the work done in displacing a particle through one meter, in the direction of a force of magnitude one Newton.
Now, we know that the power is defined as the rate of work done, or the energy supplied to a system. So it is given by
$P = \dfrac{{dW}}{{dt}}$ ……………………..(2)
The SI unit of the power is Watt.
From (2) we can say that $1$ watt is the power of a system, which consumes $1$ Joule of the energy per second.

Note: The SI unit “Joule” of the work done is accepted as an honour to the English physicist James Prescott Joule. He was the one who studied the relation between the heat and the mechanical work, which ultimately led to the law of conservation of energy. On the other hand, “Watt” is accepted as the SI unit of power in honour to the Scottish chemist James Watt, who invented the steam engine.