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Question
Estimate the total number of air molecules in a room of a capacity of 25 m3 at a temperature of 27°C.
Solution
T = 27°C + 273 = 300 K
kB = 1.38 × 10−23 J K−1
V = 25 m3
As Boltzmann’s Constant, kB = `"R"/"N"` ⇒ R = kBN
Now, PV = nRT = nkBNT
The number of molecules in the room,
nN = `"PV"/("k"_"B""T") = (1.013 xx 10^5 xx 25)/(1.38 xx 10^-23 xx 300)`
= `(25.325 xx 10^5)/(414 xx 10^-23)`
= 0.06117 × 1028
= 6.117 × 1026 molecules
nN = 6.1 × 1026 molecules
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