Physics

# An equation is given here $\left(P+\dfrac {a}{V^{2}}\right)=b\dfrac {9}{V}$ where $P=$pressure, $V=$Volume and $\theta=$Absolute temperature. if $a$ and $b$ are constants, the dimension of a will be

$[ML^{5}T^{-2}]$

##### SOLUTION

Given that,

Pressure =$P$

Volume = $V$

Absolute temperature = $\theta$

$P+\dfrac{a}{{{V}^{2}}}=\dfrac{b\theta }{V}.....(I)$

Now,

Dimension of $P= \left[ M{{L}^{-1}}{{T}^{-2}} \right]$

Dimension of $V =\left[ {{L}^{3}} \right]$

Dimension of $\theta=K$

Now, from equation (I)

$P+\dfrac{a}{{{V}^{2}}}\Rightarrow a=P{{V}^{2}}$

$a=\left[ M{{L}^{-1}}{{T}^{-2}} \right]\left[ {{L}^{6}} \right]$

$a=\left[ M{{L}^{5}}{{T}^{-2}} \right]$

Hence, the dimension of $a$ is $\left[ M{{L}^{5}}{{T}^{-2}} \right]$

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Single Correct Medium Published on 18th 08, 2020
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