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Chapter 1: Q. 1.25 (page 17)

List all the degrees of freedom, or as many as you can, for a molecule of water vapor. (Think carefully about the various ways in which the molecule can vibrate.)

Short Answer

Expert verified

Total degree of freedom for water vapor is 3.

Step by step solution

01

Given information

water vapor molecule is given.

02

Explanation

The H-O bonds enclose 105 degrees, so the molecule is definitely nonlinear.
The rotational modes are around three axes, two of them in the molecular plane and one perpendicular to it.
We can see these rotational axis in the figure as below

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Most popular questions from this chapter

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.

Use the data at the back of this book to determine ΔHfor the combustion of a mole of glucose,

C6H12O6+6O2⟶6CO2+6H2O.

This is the (net) reaction that provides most of the energy needs in our bodies.

At the back of this book is a table of thermodynamic data for selected substances at room temperature. Browse through the CPvalues in this table, and check that you can account for most of them (approximately) using the equipartition theorem. Which values seem anomalous?

In Problem 1.16 you calculated the pressure of the earth’s atmosphere as a function of altitude, assuming constant temperature. Ordinarily, however, the temperature of the bottommost 10-15 km of the atmosphere (called the troposphere) decreases with increasing altitude, due to heating from the ground (which is warmed by sunlight). If the temperature gradient |dT/dz|exceeds a certain critical value, convection will occur: Warm, low-density air will rise, while cool, high-density air sinks. The decrease of pressure with altitude causes a rising air mass to expand adiabatically and thus to cool. The condition for convection to occur is that the rising air mass must remain warmer than the surrounding air despite this adiabatic cooling.

a. Show that when an ideal gas expands adiabatically, the temperature and pressure are related by the differential equation

dTdP=2f+2TP

b. Assume that dT/dzis just at the critical value for convection to begin so that the vertical forces on a convecting air mass are always approximately in balance. Use the result of Problem 1.16(b) to find a formula for dT/dzin this case. The result should be a constant, independent of temperature and pressure, which evaluates to approximately –10°C/km. This fundamental meteorological quantity is known as the dry adiabatic lapse rate.

A cup containing 200g of water is sitting on your dining room table. After carefully measuring its temperature to be 20oC, you leave the room. Returning ten minutes later, you measure its temperature again and find that it is now 25oC. What can you conclude about the amount of heat added to the water? (Hint: This is a trick question.)
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