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Estimate the total number of air molecul...

Estimate the total number of air molecules in a room of capacity `25m^(3)` at a temperature of `27^(@)C`.

Text Solution

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`T=27^(@)C+273=300K,k_(B)=1.38xx10^(-23)JK^(-1),V=25M^(3)`
As Boltzmann.s Constant, `k_(B)=R/Nimplies Rk_(B)N`
Now , `PV=nRT=nk_(B)NT`
The number of molecules in the room,
`nN=(PV)/(k_(B)T)=(1.013xx10^(5)xx25)/(1.38xx10^(-23)xx300)`
`=(25.325xx10^(5))/(414xx10^(-23))=0.06117xx10^(28)`
`nN=6.1117xx10^(26)"molecules"`
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