Q46 / 60 · KVPY 2011 (SA) · Physics
The number of air molecules in a $(5 \mathrm{~m} \times 5 \mathrm{~m} \times 4 \mathrm{~m})$ room at standard temperature and pressure is of the order of
- A$6 \times 10^{23}$
- B$3 \times 10^{24}$
- Correct answerC$3 \times 10^{27}$
- D$6 \times 10^{30}$
Solution
$\mathrm{PV}=\mathrm{N} \times \mathrm{K} \times \mathrm{T}$
where $\mathrm{K}$ is Boltzmann constant
$\begin{array}{l}
10^{5} \times 100=\mathrm{N} \times 1.38 \times 10^{-23} \times 273 \\
\mathrm{~N} \approx 3 \times 10^{27}
\end{array}$
Hence, the correct answer is option: 'C'.