State Boyle’s law give its Mathematical Expression

State Boyle’s law give its mathematical expression

Robert Boyle, in 1662, gave this law. It relates the pressure and volume of ideal gases at constant temperature and mass.

Boyle’s Law Statement

“For a fixed mass of a gas, the volume is inversely proportional to the pressure at a constant temperature.”    

boyles law formula
boyles law formula

Thus law can also be stated as:

“For a fixed mass of a gas, the product of pressure and volume remains constant at a constant temperature.”

It means volume changes with change in pressure but product PV remains the same.

Boyle’s Law Derivation

Let the volume of a gas is V1 at pressure P1. Then

    P1V1    =          Kb        ……………… (3)

If pressure changes to P2 then the volume will change to V2 such that the product remains the same

   P2V2    =          Kb        ……………… (4)

Comparing equations (3) and (4), we can write

    P1V1    =          P2V2    ……………… (5)

Boyle’s law Experiment

Consider a gas present in a cylinder fitted with a movable and weightless piston. A manometer is attached to the cylinder to measure pressure. Let the initial volume of gas be 22.4 dm3 and the pressure on it is 1 atmosphere (as the piston has no weight on it and only air exerts pressure on it). Now place one weight on the piston, pressure will become double and it can be observed that volume is reduced to half i.e 11.2 dm3. Similarly by putting more and more weights on the piston pressure goes on increasing while volume goes on decreasing to some extent to which pressure increases. In this way, data can be collected and then by plotting graphs the law can be verified.          

boyles law experiment

The experimental data collected is given in the following table.

Boyle’s Law Experiment Conclusions

boyles law pressure volume relationship

Knowing that:

(i)        Plot of inversely proportional quantities is a hyperbolic curve.

(ii)       Plot of directly proportional quantities is a straight line.

(iii)      Plot of a constant quantity against a variable quantity, is a horizontal line.

Boyles Law Graph Explanation

We can verify the law by following three graphs.

Boyles Law Graph Explanation
Boyles Law Graphs

Figure III shows a horizontal line, meaning the pressure and volume (PV) product is constant. Thus the law is further verified.

    PV = Constant

All three plots have verified the law.

Boyle’s Law Experimental Explanation on the basis of KMT:

  Consider a cylinder fitted with a fixed piston. Let the cylinder contains the ‘n’ number of molecules at temperature ‘T’, volume is ‘V’ and pressure exerted by molecules is ‘P’.

Further, consider that piston is moved to a place where volume is reduced to half. As temperature remained the same so av. K.E remains the same and in turn, velocity remains the same. But now molecules have to travel half the distance, so the number of collisions becomes double and in turn, the pressure becomes double. It means when volume reduces to half, the pressure becomes double i.e.   V         ∝        1/P

And this is the statement of Boyle’s law.

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