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(D) The volume of a sphere is given by $V = \frac{4}{3} \pi R^3$,which implies $V \propto R^3$.When the diameter doubles,the radius $R$ also doubles $

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$7pV$

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(D) The volume of a sphere is given by $V = \frac{4}{3} \pi R^3$,which implies $V \propto R^3$.When the diameter doubles,the radius $R$ also doubles $(R ightarrow 2R)$.Therefore,the new volume $V'$ becomes $V' = \frac{4}{3} \pi (2R)^3 = 8 	imes (\frac{4}{3} \pi R^3) = 8V$.The work done against the constant atmospheric pressure $p$ during an isobaric expansion is given by $W = p \Delta V$.Substituting the values,$W = p(V' - V) = p(8V - V) = 7pV$.

Air is pumped into a balloon,of initial volume $V$,until its diameter has doubled. If the atmospheric pressure is $p$,what is the work done against the atmosphere?

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