A gas at absolute temperature 300 K has pressure p -4 - 1010 N - m 2- Boltzmann constant k -1-38 - 10-23 J - K- The number of molecules per cm 3 is of the order ofA- 1030B- 1024C- 1023D- 1027

The correct option is B 10^24From ideal gas equation, pV=NkT where N is number of molecules ∴N/V=p/kT=4×10^10/1.38×10^ 23×300 molecules/m^3 N/V=2.41×10^24 mole ...

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Standard XII

Physics

Pressure vs Velocity

A gas at abso...

Question

A gas at absolute temperature $300 K$ has pressure $p = 4 \times 10^{10} N / m^{2}$ . Boltzmann constant $k = 1.38 \times 10^{- 23} J / K$ . The number of molecules per $c m^{3}$ is of the order of

10^{30}

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10^{24}

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10^{23}

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10^{27}

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Solution

The correct option is B $10^{24}$
From ideal gas equation,
$p V = N k T$
where $N$ is number of molecules
$∴ \frac{N}{V} = \frac{p}{k T} = \frac{4 \times 10^{10}}{1.38 \times 10^{- 23} \times 300} m o l e c u l e s / m^{3}$
$⟹ \frac{N}{V} = 2.41 \times 10^{24} m o l e c u l e s / {c m}^{3}$
Which is of the order of 24.

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A gas at absolute temperature 300 K has pressure p=4×1010 N/m2. Boltzmann constant k=1.38×10−23 J/K. The number of molecules per cm3 is of the order of

The correct option is B 1024From ideal gas equation, pV=NkT where N is number of molecules ∴NV=pkT=4×10101.38×10−23×300 molecules/m3 ⟹NV=2.41×1024 molecules/cm3 Which is of the order of 24.

A gas at absolute temperature $300 K$ has pressure $p = 4 \times 10^{10} N / m^{2}$ . Boltzmann constant $k = 1.38 \times 10^{- 23} J / K$ . The number of molecules per $c m^{3}$ is of the order of