Boyle's Law

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During a diving experiment an air bubble of volume 2 cm cubed at a pressure of 4 atm rises to where pressure is 1 atm at constant temperature, so what is its new volume?

RankGuru · Accepted Answer

Boyle's law, described in NCERT Class 11, Chapter 13 (Kinetic Theory), states that for a fixed mass of gas held at constant temperature the pressure and volume are inversely related, expressed as $P_1V_1 = P_2V_2$. As the bubble rises through the water the surrounding pressure drops from 4 atm to 1 atm while the temperature stays constant, so we can equate the products directly. Substituting the values gives $4 	imes 2 = 1 	imes V_2$, hence $V_2 = 8$ cm cubed, meaning the bubble expands to four times its original size. The option 0.5 cm cubed applies the proportionality backwards, as though pressure and volume increased together. The option 2 cm cubed wrongly assumes volume is unaffected by pressure change. The option 4 cm cubed underestimates the expansion by using a factor of 2 rather than the true pressure ratio of 4. A magnitude check supports the result: since pressure fell to one quarter, volume must rise by the same factor, and $2 	imes 4 = 8$ cm cubed confirms both the direction and size of the change.

Boyle's Law

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