Question

Please find below the ​

Answer 1

Explanation:

Given -

• $\mathsf{(p + \dfrac{a}{ {V}^{2} }) (V - b) = RT}$

Here,

p = pressure

V = volume

T = absolute temperature

a, b, R = constant

To Find -

• Dimension of a.b = ?

From Dimensional analysis :-

$\mathsf{p = \dfrac{a}{ {V}^{2} } }$

Then,

a = pV²

As we know that :-

$\mathsf{pressure = \dfrac{F}{A} }$

$\mathsf{ \frac{MLT {}^{ - 2} }{L {}^{2} } }$

$\mathsf{p = ML {}^{ - 1} T {}^{ - 2} }$

Then,

$\mathsf{a = ML {}^{ - 1} T {}^{ - 2} \times {(L {}^{3}) }^{2} }$

$\mathsf{a = ML {}^{ - 1} T {}^{ - 2} \times {L}^{6} }$

Hence,

$\mathsf{a = ML {}^{5} {T}^{ - 2} }$

And

V = b

As we know that :-

• V (volume) = L³

Hence,

b = L³

Then,

The value of a.b is

$\mathsf{a . b = ML {}^{5} T {}^{ - 2} \times L {}^{3} }$

Hence,

$\mathsf{a.b =ML {}^{8} T {}^{ - 2} }$

Therefore,

Option B is correct.