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Chapter 9: Problem 1276

The speeds of 5 molecules of a gas (in arbitrary units) are as follows: \(2,3,4,5,6\), The root mean square speed for these molecules is (A) \(4.24\) (B) \(2.91\) (C) \(4.0\) (D) \(3.52\)

Short Answer

Expert verified
The root mean square speed for these molecules is (A) \(4.24\).

Step by step solution

01

Square each speed

First, we find the square of each speed given in the problem. These are: \(2^2 = 4\), \(3^2 = 9\), \(4^2 = 16\), \(5^2 = 25\), and \(6^2= 36\).
02

Find the mean of the squared speeds

Now, we will find the mean of the squared speeds: \[(4 + 9 + 16 + 25 + 36) \div 5\] \[= \frac{90}{5}\] \[= 18\]
03

Find the square root of the mean

Finally, we will find the square root of the mean we calculated in step 2: \[\sqrt{18} \approx 4.24\]
04

Compare the calculated value with the options

Now, we will compare our calculated value with the given options: (A) \(4.24\) (B) \(2.91\) (C) \(4.0\) (D) \(3.52\) Our calculated value \(\approx 4.24\), which matches option (A), so the correct answer is (A) \(4.24\).

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Most popular questions from this chapter

A perfect gas at \(27^{\circ} \mathrm{C}\) is heated at constant pressure to \(327^{\circ} \mathrm{C}\). If original volume of gas at \(27^{\circ} \mathrm{C}\) is \(\mathrm{V}\) then volume at \(327^{\circ} \mathrm{C}\) is (A) \(2 \mathrm{~V}\) (B) \(\mathrm{V}\) (C) (V/2) (D) \(3 \mathrm{~V}\)

A gas at \(27{ }^{\circ} \mathrm{C}\) temperature and 30 atmospheric pressure $1 \mathrm{~s}$ allowed to expand to the atmospheric pressure if the volume becomes two times its initial volume, then the final temperature becomes (A) \(273^{\circ} \mathrm{C}\) (B) \(-173^{\circ} \mathrm{C}\) (C) \(173^{\circ} \mathrm{C}\) (D) \(100^{\circ} \mathrm{C}\)

The temperature of an ideal gas is increased from \(27^{\circ} \mathrm{C}\) to \(927^{\circ} \mathrm{C}\). The root mean square speed of its molecules becomes (A) Four times (B) One-fourth (C) Half (D) Twice

If the ratio of vapor density for hydrogen and oxygen is \([1 /(16)]\), then under constant pressure the ratio of their \(\mathrm{rms}\) velocities will be (A) \(4: 1\) (B) \(1: 16\) (C) \(16: 1\) (D) \(1: 4\)

The average translational energy and \(\mathrm{rms}\) speed of molecules in sample of oxygen gas at \(300 \mathrm{~K}\) are $6.21 \times 10^{-21} \mathrm{~J}\( and \)484 \mathrm{~m} / \mathrm{s}$ respectively. The corresponding values at \(600 \mathrm{~K}\) are nearly (assuming ideal gas behavior) (A) \(6.21 \times 10^{-21} \mathrm{~J}, 968 \mathrm{~m} / \mathrm{s}\) (B) \(12.42 \times 10^{-21} \mathrm{~J}, 684 \mathrm{~m} / \mathrm{s}\) (C) \(12.42 \times 10^{-21} \mathrm{~J}, 968 \mathrm{~m} / \mathrm{s}\) (D) \(8.78 \times 10^{-21} \mathrm{~J}, 684 \mathrm{~m} / \mathrm{s}\)
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