Question

Obtain the demensional formula for R used in the ideal gas
equation PV = RT.
Define power, write its S.1 unit.​

Answer 1

Explanation:

Dimensional Formula of R

PV = RT

$PV = RT \\ \\ R = \frac{PV}{T} \\ \\ = \frac{ML {}^{ - 1} T {}^{ - 2} \times L {}^{3} }{ k} \\ \\ ML {}^{2} T {}^{ - 2} k {}^{ - 1}$

Power -

The Rate of doing work is called power

It's SI Unit is Watt ( W )

$Power = \frac{energy}{time} \\ \\ = \frac{ML {}^{2} T {}^{ - 2} }{T} \\ \\ ML {}^{2} T {}^{ - 3}$

Answer 2

Answer:

From ideal gas equation we have :

P V = R T  [ For n = 1 ]

$\sf R = \dfrac{P \ V}T}$

$\sf \longrightarrow \dfrac{P \ V}{T} = \dfrac{F}{A} . \dfrac{V}{T}$

We know dimension of :

$\sf F= \left[M \ L \ T^{-2} \right ]$

$\sf V= \left[L^3 \right ]$

$\sf A= \left[L^2 \right ]$

$\sf T= \left[K \right ]$

Now dimension of R :

$\sf R = \dfrac{\left[MLT^{-2} \right].\left[L^3 \right]}{\left[L^2 \right].\left[K \right]}$

$\sf R=\left[M \ L^2 \ T^{-2} \ K^{-1} \right]$

Power :

It is define as rate of transfer of energy .

$\sf P=\dfrac{Work \ done}{Time \ taken}$

SI unit of power is watt.