Question

The equation (P + a/v2) (V-b) = constant. The units of a is :
A) Dyne * cm5
B) Dyne * cm4
C) Dyne * cm3
D) Dyne * cm2

Answer 1

For the unit of ‘a' -

By, taking the terms (P + a/v^2) from the equation,


Unit of ‘P' (Pressure) = Unit of ‘a' / Unit of ‘V^2' (Volume) (CGS System)

Unit of ‘a' = Unit of (P×V^2)

= (g - cm^-1 - s^-2)× (cm^3)^2

= g - cm^-1 - cm^6 - s^-2

= g - cm^5 - s^-2

= (g - cm - s^-2) × cm^4

Because, g-cm-s^-2 = Dyne

So,

Unit of ‘a' = Dyne × cm^4.........●



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Answer 2

Answer:

The unit of a is    $Dyne \: \times {cm}^{4}$ .

Explanation:

Given term,

$(p + \frac{a}{ {v}^{2} } )(v - b) = constant$

$where \: p \: is \: pressure \: \\ and \: v \: is \: volume \: \\ a \: and \: b \: are \: constant$

We know,

$P= \frac{F}{A} = Dyne/ {cm}^{2}$

$\frac{a}{ {v}^{2} } = 1/ { ({cm}^{3}) }^{2}$

Now, the unit of p =  unit of $\frac{a}{v^2}$  [From dimension analysis]

The units of 'a'  is given by,

                                           $\frac{Dyne}{ {cm}^{2} } \times { {(cm}^{3}) }^{2}$

                                          =  $Dyne \: \times {cm}^{4}$

              ∴  The unit of a is    $Dyne \: \times {cm}^{4}$