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Chapter 20: Q. 8 (page 566)

The two containers of gas in FIGURE Q20.8 are in good thermal
contact with each other but well insulated from the environment. They
have been in contact for a long time and are in thermal equilibrium.
a. Is vrms of helium greater than, less than, or equal to vrms of
argon? Explain.
b. Does the helium have more thermal energy, less thermal
energy, or the same amount of thermal energy as the argon?
Explain.

Short Answer

Expert verified

The solution gives thermal equilibrium

good thermal

contact with each other

Step by step solution

01

Description on thermal energy

It deals with the energy related to the temperature.

02

Description on the solution

Provided solution $ν r m s = \sqrt{\frac{3 k b T}{{m_{m o l e c u l e s}}_{}}} ν r m s \infty \sqrt{T}, ν r m s \infty \frac{1}{\sqrt{m_{m o l e c u l e s}}}$

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Most popular questions from this chapter

$1.0 m o l$ of a monatomic gas interacts thermally with $1.0 m o l$ of an elemental solid. The gas temperature decreases by $50^{o} C$ at constant volume. What is the temperature change of the solid?

The density of air at STP is about $\frac{1}{1000}$ the density of water. How does the average distance between air molecules compare to the average distance between water molecules? Explain.

Consider a container like that shown in Figure $20.12$ , with $n_{1}$ moles of a monatomic gas on one side and $n_{2}$ moles of a diatomic gas on the other. The monatomic gas has initial temperature $T_{1 i}$ . The diatomic gas has initial temperature $T_{2 i}$ .
a. Show that the equilibrium thermal energies are

$\begin{aligned} E_{1 f} = \frac{3 n_{1}}{3 n_{1} + 5 n_{2}} (E_{1 i} + E_{2 i}) \\ E_{2 f} = \frac{5 n_{2}}{3 n_{1} + 5 n_{2}} (E_{1 i} + E_{2 i}) \end{aligned}$

b. Show that the equilibrium temperature is

$T_{f} = \frac{3 n_{1} T_{1 i} + 5 n_{2} T_{2 i}}{3 n_{1} + 5 n_{2}}$

c. $2.0 g$ of helium at an initial temperature of role="math" localid="1648474536876" $300 K$ interacts thermally with $8.0 g$ of oxygen at an initial temperature of $600 K$ . What is the final temperature? How much heat energy is transferred, and in which direction?

Integrated circuits are manufactured in vacuum chambers in which the air pressure is $1.0 \times 10^{- 10} mm$ of $Hg$ . What are (a) the number density and (b) the mean free path of a molecule? Assume $T = 20 ° C$ .

At what temperature does the $r m s$ speed of $(a)$ a nitrogen molecule and $(b)$ a hydrogen molecule equal the escape speed from the earth's surface? $(c)$ You'll find that these temperatures are very high, so you might think that the earth's gravity could easily contain both gases. But not all molecules move with $V_{r m s}$ . There is a distribution of speeds, and a small percentage of molecules have speeds several times $V_{r m s}$ . Bit by bit, a gas can slowly leak out of the atmosphere as its fastest molecules escape. A reasonable rule of thumb is that the earth's gravity can contain a gas only if the average translational kinetic energy per molecule is less than $1 %$ of the kinetic energy needed to escape. Use this rule to show why the earth's atmosphere contains nitrogen but not hydrogen, even though hydrogen is the most abundant element in the universe.

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