Question 874: Thermodynamics & KTG

Question

An ideal gas in a container of volume 500 c.c. is at a pressure of $$2 	imes 10^{+5} \mathrm{~N} / \mathrm{m}^2$$. The average kinetic energy of each molecule is $$6 	imes 10^{-21} \mathrm{~J}$$. The number of gas molecules in the container is

Accepted Answer

$$\mathrm{PV}=\mathrm{Nk}_{\mathrm{B}} \mathrm{T}$$
and, K.E./molecule $$=\frac{3}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}=\frac{3}{2} \frac{\mathrm{PV}}{\mathrm{N}}$$
$$\begin{aligned}
	herefore \quad \mathrm{N} & =\frac{3}{2} 	imes \frac{\mathrm{PV}}{(	ext { K.E./molecule })} \
& =\frac{3}{2} 	imes \frac{2 	imes 10^5 	imes 500 	imes 10^{-6}}{6 	imes 10^{-21}}=2.5 	imes 10^{22}
\end{aligned}$$

Answer

$$5 	imes 10^{25}$$

Answer

$$5 	imes 10^{23}$$

Answer

$$25 	imes 10^{23}$$

Answer

$$2.5 	imes 10^{22}$$

Thermodynamics & KTG

An ideal gas in a container of volume 500 c.c. is at a pressure of $2 \times 10^{+5} \mathrm{~N} / \mathrm{m}^2. The average kinetic energy of each molecule is 6 \times 10^{-21} \mathrm{~J}$. The number of gas molecules in the container is

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