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The graph between pressure and volume in Boyle’s law experiment is shown in figure for different masses of same gas at same temperature then:

(A) $m_{2}>m_{1}$
(B) $m_{1}>m_{2}$
(C) $m_{1}=m_{2}$
(D) $m_{1}^{3}>m_{2}$

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Last updated date: 23rd Feb 2024
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IVSAT 2024
Answer
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Hint: We know that Boyle's law states that at constant temperature for a fixed mass, the absolute pressure and the volume of a gas are inversely proportional. The law can also be stated in a slightly different manner, that the product of absolute pressure and volume is always constant. The volume of the air in the system can be altered by moving the piston. By considering the air as an ideal gas, the pressure and the volume readings allow a direct verification of Boyle's law at various temperatures.

Complete step by step answer
We can say that an ideal gas is a gas that conforms, in physical behaviour, to a particular, idealized relation between pressure, volume, and temperature called the ideal gas law. The equation of state of n gram-moles of a perfect gas can then be written as $\mathrm{pv} / \mathrm{t}=\mathrm{nR},$ in which $\mathrm{R}$ is called the universal gas constant.
We know that from ideal gas equation, $\mathrm{PV}=\mathrm{nRT}$ and $\mathrm{n}=\dfrac{\mathrm{w}}{\mathrm{M}}$ where $\mathrm{M}$ is the molecular weight of the gas.
Now we can say that $\mathrm{PV}=\dfrac{\mathrm{w}}{\mathrm{M}} \mathrm{RT}$
So, we draw a vertical line at a volume of say $\mathrm{V}_{0}$.
Then for this volume, we see that pressure is higher for the gas with molecular weight as $\mathrm{M}_{2}$ (from the graph)
Hence, this means that $\mathrm{M}_{2}$ must be smaller than $\mathrm{M}_{1}$.

So, the correct answer is option B.

Note: We know that since the boiling point is dependent on pressure, we can use Boyle's law and a syringe to make water boil at room temperature. Deep-sea fish die when they're brought from the depths to the surface. The pressure decreases dramatically as they are raised, increasing the volume of gases in their blood and swim bladder. The law itself can be stated as follows for a fixed mass of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional. Or Boyle's law is a gas law, stating that the pressure and volume of a gas have an inverse relationship.