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Chapter 9: Problem 1329

For a gas \(\gamma=(7 / 5)\), the gas may probably be (A) Neon (B) Argon (C) Helium (D) Hydrogen

Short Answer

Expert verified
The gas with a specific heat ratio \(\gamma = \frac{7}{5}\) (1.4) is (D) Hydrogen, as it has 5 degrees of freedom.

Step by step solution

01

Find the degrees of freedom for each gas

The specific heat ratio is related to the degrees of freedom (f) of the gas particles, which is defined as the number of independent ways in which a gas particle's energy can be partitioned. Every gas has a unique number of degrees of freedom, which can be calculated using the following formula: For a polyatomic gas with f degrees of freedom, \[\gamma = 1 + \frac{2}{f}\] Our task is to find the correct gas with \(\gamma = \frac{7}{5}\).
02

Determine the degrees of freedom for the given value of gamma

Knowing that \(\gamma = 1.4\), we can use the polyatomic gas formula to determine the degrees of freedom: \(1.4 = 1 +\frac{2}{f}\) Now, solve for f: \(0.4 =\frac{2}{f}\) \(\Rightarrow f = 5\) So, the gas we are looking for must have 5 degrees of freedom.
03

Identify the correct gas based on degrees of freedom

We can now evaluate the options given: (A) Neon (B) Argon (C) Helium (D) Hydrogen Here are the degrees of freedom for each gas and its molecular structure: (A) Neon (Ne): Monoatomic, 3 degrees of freedom (B) Argon (Ar): Monoatomic, 3 degrees of freedom (C) Helium (He): Monoatomic, 3 degrees of freedom (D) Hydrogen (H₂): Diatomic, 5 degrees of freedom Based on the degrees of freedom, we can now determine that the correct answer is: (D) Hydrogen

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Most popular questions from this chapter

The temperature at which the rms speed of hydrogen molecules is equal to escape velocity on earth surface will be (A) \(5030 \mathrm{~K}\) (B) \(10063 \mathrm{~K}\) (C) \(1060 \mathrm{~K}\) D) \(8270 \mathrm{~K}\)

At what temperature pressure remaining constant will the \(\mathrm{rms}\) speed of a gas molecules increase by \(10 \%\) of the \(\mathrm{rms}\) speed at NTP? (A) \(57.3 \mathrm{~K}\) (B) \(57.3^{\circ} \mathrm{C}\) (C) \(557.3 \mathrm{~K}\) (D) \(-57.3^{\circ} \mathrm{C}\)

For a gas, the rms speed at \(800 \mathrm{~K}\) is (A) Four times the value at \(200 \mathrm{~K}\) (B) Twice the value at \(200 \mathrm{~K}\) (C) Half the value at \(200 \mathrm{~K}\) (D) same as at \(200 \mathrm{~K}\)

If \(\mathrm{rms}\) speed of a gas is $\mathrm{v}_{\mathrm{rms}}=1840 \mathrm{~m} / \mathrm{s}\( and its density \)\rho=8.99 \times 10^{-2} \mathrm{~kg} / \mathrm{m}^{3}$, the pressure of the gas will be (A) \(1.01 \times 10^{3} \mathrm{Nm}^{-2}\) (B) \(1.01 \times 10^{5} \mathrm{Nm}^{-2}\) (C) \(1.01 \times 10^{7} \mathrm{Nm}^{-2}\) (D) \(1.01 \mathrm{Nm}^{-2}\)

A cylinder contains \(10 \mathrm{~kg}\) of gas at pressure of $10^{\prime} \mathrm{N} / \mathrm{m}^{2}$. The quantity of gas taken out of the cylinder, if final pressure is \(2.5 \times 10^{6} \mathrm{Nm}^{-2}\). will be (temperature of gas is constant) (A) \(5.2 \mathrm{~kg}\) (B) \(3.7 \mathrm{~kg}\) (C) \(7.5 \mathrm{~kg}\) (D) \(1 \mathrm{~kg}\)
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