Question

It has been suggested that for liquids s3 Beta^= K, is a constant, with s being the surface tension and beta the compressibility, show that K is not a dimensionless constant.

Answer 1

Explanation:

s=F/L

and B=A/F

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Hope it helps

Answer 2

Answer:

The constant K is not dimensionless has been proved.

Explanation:

Given Data:
$s^{3}\beta ^{4} = K$

where s is the surface tension, k is the constant, and β is the compressibility.

To Find:
To demonstrate that the constant K is not a dimensionless one.

Calculations:

Surface Tension is given by the ratio of Force to Length.

So, the dimensional formula for Surface Tension is given by

$[S] = M^{1} L^{0} T^{-2}$

Compressibility ( β ) is given by the reciprocal of pressure.

So, the dimensional formula for compressibility will be

$[\beta] = M^{-1} L^{1} T^{2}$

Now, According to the question, we have

$s^{3}\beta ^{4} = K$

Putting the values of the dimensional formula into the given equation, we have

$[s^{3}\beta ^{4} ] = [M^{3} L^{0} T^{-6} ][M^{-4} L^{4} T^{8} ] = [M^{-1} L^{4} T^{2} ]$

Therefore, From this, we get that the constant K is not dimensionless.

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