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Chapter 1: Q. 1.19 (page 13)
Suppose you have a gas containing hydrogen molecules and oxygen molecules, in thermal equilibrium. Which molecules are moving faster, on average? By what factor?
Hydrogen molecule will be moving faster
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When you're sick with a fever and you take your temperature with a thermometer, approximately what is the relaxation time?
For a solid, we also define the linear thermal expansion coefficient, 伪, as the fractional increase in length per degree:
(a) For steel, 伪 is 1.1 x 10-5 K-1. Estimate the total variation in length of a 1 km steel bridge between a cold winter night and a hot summer day.
(b) The dial thermometer in Figure 1.2 uses a coiled metal strip made of two different metals laminated together. Explain how this works.
(c) Prove that the volume thermal expansion coefficient of a solid is equal to the sum of its linear expansion coefficients in the three directions 尾=伪x + 伪y + 伪z. (So for an isotropic solid, which expands the same in all directions, 尾 =3 伪 .)
Look up the enthalpy of formation of atomic hydrogen in the back of this book. This is the enthalpy change when a mole of atomic hydrogen is formed by dissociating mole of molecular hydrogen (the more stable state of the element). From this number, determine the energy needed to dissociate a single molecule, in electron-volts.
In analogy with the thermal conductivity, derive an approximate formula for the viscosity of an ideal gas in terms of its density, mean free path, and average thermal speed. Show explicitly that the viscosity is independent of pressure and proportional to the square root of the temperature. Evaluate your formula numerically for air at room temperature and compare to the experimental value quoted in the text.
Suppose you open a bottle of perfume at one end of a room. Very roughly, how much time would pass before a person at the other end of the room could smell the perfume, if diffusion were the only transport mechanism? Do you think diffusion is the dominant transport mechanism in this situation?
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