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  • 2 moles of air was present in a balloon with a diameter of 1m at 1 atm. On further addition of air, the pressure increased to 6 atm. The pressure at each point is directly related to the

2 moles of air was present in a balloon with a diameter of 1m at 1 atm. On further addition of air, the pressure increased to 6 atm. The pressure at each point is directly related to the diameter of the balloon. Calculate the moles of air added for the given change in pressure.

Option: 1

80


Option: 2

256


Option: 3

2592


Option: 4

3008


Answers (1)

best_answer

\mathrm{\begin{aligned} & P \propto d \\ & P=k d \\ & k=\frac{1 a t m}{1 m e t e r} \\ & P V=n R T \\ & k d\left(\frac{4}{3} \pi r^3\right)=n R T \\ & \left.k d f \frac{1}{6} \pi d^3\right)=n R T \\ & \frac{d_1^4}{d_2^4}=\frac{n_1}{n_2} \\ & \frac{1^4}{6^4}=\frac{2}{n_2} \\ & n_2=2 \times 6^4 \\ & =2592 \end{aligned}}

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