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# What will be the S.I. unit of power ?

Last updated date: 18th Sep 2024
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Hint: Let us write the formula power because after expanding that we can easily calculate the unit of power.

As we know that power is the amount of energy transferred or converted per unit time.
And heat is denoted as P.

As we know that formula of power that P = $\dfrac{{\text{Q}}}{{\Delta {\text{T}}}}$
Where Q is the heat of the body.

And $\Delta {\text{T}}$ is the change in temperature. So, unit of $\Delta {\text{T}}$ will be the unit of temperature that is kelvin (k)

And we know that formula of heat of the body is Q = mC$\Delta {\text{T}}$

Where m is the mass of the body. So, its unit will be kilogram (kg).

C is specific heat. And unit of joule per kilogram kelvin $\left( {J/kg \times k} \right)$.

And $\Delta {\text{T}}$ is the change in temperature. So, unit of $\Delta {\text{T}}$ will be the unit of temperature that is kelvin (k)

Now unit of heat of the body is = mC$\Delta {\text{T}}$ = $kg \times \dfrac{J}{{kg \times k}} \times k$ = J (Joule)

So, the S.I unit of the heat of the body will be Joule (J).

Now the S.I unit of power will be P = $\dfrac{{\text{Q}}}{{\Delta {\text{T}}}} = \dfrac{{\text{J}}}{{\Delta {\text{T}}}} = {\text{W}}$(Watt)

So, the S.I unit of power is Watt (W).

Note: Whenever we come up with this type of problem where we are asked to find the unit of any quantity. Then we first write the formula to calculate that quantity and then in place of values we put the unit of every quantity. After solving that we will get the required S.I. unit asked for that quantity (here power).