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Chapter 1: Q. 1.18 (page 13)
Calculate the rms speed of a nitrogen molecule at room temperature.
Root mean square speed is 515.9m/s.
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The Fahrenheit temperature scale is defined so that ice melts at 320 F and water boils at 2120 F.
(a) Derive the formula for converting from Fahrenheit to Celsius and back
(b) What is absolute zero on the Fahrenheit scale?
In Problem 1.16 you calculated the pressure of earth's atmosphere as a function of altitude, assuming constant temperature. Ordinarily, however, the temperature of the bottom most 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
(b) Assume that dT/dz is 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 1.16b to find a formula for dT/dz in this case. The result should be a constant, independent of temperature and pressure, which evaluates to approximately -10oC/ km. This fundamental meteorological quantity is known as the dry adiabatic lapse rate.
A mole is approximately the number of protons in a gram of protons. The mass of a neutron is about the same as the mass of a proton, while the mass of an electron is usually negligible in comparison, so if you know the total number of protons and neutrons in a molecule(i,e., its "atomic mass"), you know the approximate mass(in grams) of a mole of these molecules. Referring to the periodic table at the back of this book ,find the mass of a mole of each of the following : Water, nitrogen (N2), lead, quartz (Si O2)
When spring finally arrives in the mountains, the snow pack may be two meters deep, composed of ice and of air. Direct sunlight provides about to earth's surface, but the snow might reflect of this energy. Estimate how many weeks the snow pack should last, if direct solar radiation is the only source of energy.
Problem 1.49. Consider the combustion of one mole of with mole of under standard conditions, as discussed in the text. How much of the heat energy produced comes from a decrease in the internal energy of the system, and how much comes from work done by the collapsing atmosphere? (Treat the volume of the liquid water as negligible.)
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