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Chapter 9: Problem 1315

A monoatomic gas molecule has (A) Three degrees of freedom (B) Five degrees of freedom (C) Six degrees of freedom (D) Four degrees of freedom

Short Answer

Expert verified
A monoatomic gas molecule has three degrees of freedom, which are contributed by the translational motions along the x, y, and z directions. As monoatomic gas molecules are spherical and do not have any covalent bonds, they do not possess any rotational or vibrational degrees of freedom. Therefore, the answer is (A) Three degrees of freedom.

Step by step solution

01

Translational degrees of freedom for monoatomic gas molecules

A molecule can move independently along the three spatial directions - x, y, and z. So, the total number of translational degrees of freedom for a monoatomic gas molecule is 3.
02

Rotational degrees of freedom for monoatomic gas molecules

Rotational degrees of freedom refer to the number of independent ways in which a molecule can rotate. Monoatomic gas molecules are spherical and rotations about the center of mass do not change the position of any atomic nuclei. Since these rotations do not store any energy, monoatomic gas molecules do not possess any rotational degrees of freedom.
03

Calculating the total degrees of freedom

Now, we combine the translational and rotational degrees of freedom calculated in Steps 1 and 2. Total degrees of freedom = (translational degrees of freedom) + (rotational degrees of freedom) = 3 + 0 = 3 So, the monoatomic gas molecules have: (A) Three degrees of freedom

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Most popular questions from this chapter

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 (B) \(-173^{\circ} \mathrm{C}\) (A) \(273^{\circ} \mathrm{C}\) (C) \(173^{\circ} \mathrm{C}\) (D) \(100^{\circ} \mathrm{C}\)

A cylinder of capacity 20 liters is filled with \(\mathrm{H}_{2}\) gas. The total average kinetic energy of translator motion of its molecules is $1.5 \times 10^{5} \mathrm{~J}$. The pressure of hydrogen in the cylinder is (A) \(4 \times 10^{6} \mathrm{Nm}^{-2}\) (B) \(3 \times 10^{6} \mathrm{Nm}^{-2}\) (C) \(5 \times 10^{6} \mathrm{Nm}^{-2}\) (D) \(2 \times 10^{6} \mathrm{Nm}^{-2}\)

The specific heats at constant pressure is greater than that of the same gas at constant volume because (A) At constant volume work is done in expanding the gas. (B) At constant pressure work is done in expanding the gas. (C) The molecular vibration increases more at constant pressure. (D) The molecular attraction increases more at constant pressure.

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

When the temperature of a gas is raised from \(27^{\circ} \mathrm{C}\) to \(90^{\circ} \mathrm{C}\), the percentage increase in the rms velocity of the molecules will be (A) \(15 \%\) (B) \(17.5 \%\) (C) \(10 \%\) (D) \(20 \%\)
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