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


ANSWER

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


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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