The number of air molecules in a (5 ,m times | vedclass

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(C) The volume of the room is $V = 5 \,m 	imes 5 \,m 	imes 4 \,m = 100 \,m^3$.At standard temperature and pressure $(STP)$,the pressure $p = 1.013 \

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$3 	imes 10^{27}$

Vedclass · Answer

(C) The volume of the room is $V = 5 \,m 	imes 5 \,m 	imes 4 \,m = 100 \,m^3$.At standard temperature and pressure $(STP)$,the pressure $p = 1.013 	imes 10^5 \,Pa \approx 10^5 \,Pa$ and temperature $T = 273 \,K$.The Boltzmann constant $k_B = 1.38 	imes 10^{-23} \,J/K$.Using the ideal gas equation $pV = Nk_BT$,the number of molecules $N$ is given by $N = \frac{pV}{k_BT}$.Substituting the values: $N = \frac{10^5 	imes 100}{1.38 	imes 10^{-23} 	imes 273} \approx \frac{10^7}{3.7674 	imes 10^{-21}} \approx 2.65 	imes 10^{27}$.Rounding to the nearest order of magnitude,$N \approx 3 	imes 10^{27}$ molecules.

The number of air molecules in a $(5 \,m \times 5 \,m \times 4 \,m)$ room at standard temperature and pressure is of the order of

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