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III 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 T1li. The diatomic gas has initial temperature \(T_{2 \mathrm{i}}\).

a. Show that the equilibrium thermal energies are

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Most popular questions from this chapter

Uranium has two naturally occurring isotopes. U238 has a natural abundance of 99.3% andU235 has an abundance of 0.7%. It is the rarer U235that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride, role="math" UF6, which is a gas, then allowing it to diffuse through a series of porous membranes. UF6235 has a slightly larger rms speed than UF6238 and diffuses slightly faster. Many repetitions of this procedure gradually separate the two isotopes. What is the ratio of the rms speed of UF6235 to that ofUF6238?

Suppose you double the temperature of a gas at constant volume. Do the following change? If so, by what factor?

a. The average translational kinetic energy of a mole cule.

b. The rms speed of a molecule.

c. The mean free path.

Equation 20.3is the mean free path of a particle through a gas of identical particles of equal radius. An electron can be thought of as a point particle with zero radius.

a. Find an expression for the mean free path of an electron through a gas.

b. Electrons travel 3kmthrough the Stanford Linear Accelerator. In order for scattering losses to be negligible, the pressure inside the accelerator tube must be reduced to the point where the mean free path is at least 50km. What is the maximum possible pressure inside the accelerator tube, assuming T=20°C?Give your answer in both Paand atm.

2.0gof helium at an initial temperature of 300Kinteracts thermally with 8.0gof oxygen at an initial temperature of 600K.

a. What is the initial thermal energy of each gas?

b. What is the final thermal energy of each gas?

c. How much heat energy is transferred, and in which direction?

d. What is the final temperature?

A monatomic gas is adiabatically compressed to 18of its initial volume. Does each of the following quantities change? If so, does it increase or decrease, and by what factor? If not, why not?

a. The rmsspeed.

b. The mean free path.

c. The thermal energy of the gas.

d. The molar specific heat at constant volume.

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