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  • A container with a volume of 0.03 m3 holds a gas at a temperature of 400 K. The gas molecules have a mass of 4.5 × 10−26 kg. Calculate the average force exerted by

A container with a volume of 0.03 m3 holds a gas at a temperature of 400 K. The gas molecules have a mass of 4.5 × 10−26 kg. Calculate the average force exerted by the gas molecules on the walls of the container and determine the pressure inside the container.

 

Option: 1

1.458 ×10−9 Pa


Option: 2

3.283 ×10−13 Pa


Option: 3

2.451 ×10−16 Pa


Option: 4

3.145 ×10−17 Pa


Answers (1)

best_answer

Given data: Volume of the container (V ) = 0.03 m3

Temperature (T) = 400 K

Mass of each gas molecule (m) = 4.5 × 10−26 kg

Boltzmann constant (k) = 1.38 × 10−23 J/K

Step 1: Calculate the average velocity of the gas molecules using the formula:

\langle v\rangle=\sqrt{\frac{8 k T}{\pi m}}

Substitute the given values and solve for ⟨v⟩:

\begin{gathered} \langle v\rangle=\sqrt{\frac{8 \times 1.38 \times 10^{-23} \times 400}{\pi \times 4.5 \times 10^{-26}}} \\ \langle v\rangle \approx 435.03 \mathrm{~m} / \mathrm{s} \end{gathered}

Step 2: Calculate the average force (Favg) exerted by the gas molecules on the walls of the container using the formula:

F_{\text {avg }}=2 m N\langle v\rangle^2 V^{-1}

Substitute the given values and solve for Favg:

\begin{gathered} F_{\text {avg }}=2 \times 4.5 \times 10^{-26} \times N \times(435.03)^2 \times \frac{1}{0.03} \\ F_{\text {avg }} \approx 5.926 \times 10^{-15} \mathrm{~N} \end{gathered}Step 3: Calculate the pressure (P) inside the container using the formula:

P=\frac{F_{\mathrm{avg}}}{A}

where A is the area of one of the container’s walls. Since the container is closed and has six walls, A = 6V (total surface area). Substitute the values of Favg and V and solve for P:

\begin{gathered} P=\frac{5.926 \times 10^{-15}}{6 \times 0.03} \\ P \approx 3.283 \times 10^{-13} \mathrm{~Pa} \end{gathered}

Therefore, the correct option is (2).

 

Posted by

shivangi.shekhar

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