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A spherical balloon of volume V contains helium at a pressure P. How many moles of helium are in the balloon if the average kinetic energy of the helium atoms is $K$ ?

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$\frac{2 PV}{{KN}_{4}}$

$\frac{3 PV}{{KN}_{4}}$

$\frac{5 PV}{3 {KN}_{A}}$

$\frac{3 PV}{2 {KN}_{A}}$

answer is D.

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Detailed Solution

$P = \frac{2 N}{3 V} K$ from the kineitc-theory account for pressure.

$N = \frac{3}{2} \frac{PV}{K}$

n = $\frac{N}{N_{A}} = \frac{3}{2} \frac{PV}{{KN}_{A}}$

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