First slide

Kinetic theory of ideal gases

Question

Number of molecules in a volume of $4 c m^{3}$ of a perfect mono atomic gas at some temperature T and at a pressure of $2 c m$ of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is $4 \times 10^{- 14} e r g, g = 980 c m / s^{2}, d e n s i t y o f m e r c u r y = 13 .6 g / c m^{3})$

Moderate

A

$5.8 \times 10^{16}$
B

$4.0 \times 10^{16}$
C

$4.0 \times 10^{18}$
D

$5.8 \times 10^{18}$

Solution

$\begin{array}{l} No of molecules=N= \frac{PV}{KT} \{K=Boltzman Constant\} \\ \begin{array}{l} \Rightarrow N= \frac{{2hρ}_{H g} g}{KT} \\ \Rightarrow N= \frac{2 (4) . (13.6) (980)}{\frac{2}{3} (K.E)}, [We know \frac{3}{2} KT=K.E] \\ \Rightarrow N = \frac{3 \times 13.6 \times (980) (4)}{4 \times 10^{- 14}} {=4×10}^{18} \end{array} \end{array}$

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