Question

Which of the following is correct mathematical interpretation of Boyle's law?

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

Boyle's Law describes the pressure-volume relationship of gases at room temperature.

The law states that the volume of a fixed mass of gas is inversely proportional to its pressure at constant temperature.

Mathematically, the law may be expressed as $P\propto \frac{1}{v}$(at constant temperature and mass) Or $P=K\times \frac{1}{v}$ where K is the proportionality constant.

The value of K depends on the amount of gas, temperature of gas, and units in which P and V are expressed. On rearranging Eq. (ii), we get ... (iii)

It means that at a constant temperature, the product of the pressure and volume of a fixed amount of gas is constant.

If a fixed amount of gas at constant temperature T occupying volume $V_1$ at pressure $P_1$ undergoes expansion so that the volume becomes $V_2$ and the pressure becomes $P_2$, then according to Boyle's law

$\frac{P_1}{P_2}=\frac{V_2}{V_1}$ (T and n are constants)