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Chapter 1: Q 1.5. (page 5)
When you're sick with a fever and you take your temperature with a thermometer, approximately what is the relaxation time?
1 minute.
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The enthalpy of combustion of a gallon ( liters) of gasoline is about . The enthalpy of combustion of an ounce of corn flakes is about. Compare the cost of gasoline to the cost of corn flakes, per calorie.
According to a standard reference table, the R value of a 3.5 inch-thick vertical air space (within a wall) is 1.0 R in English units), while the R value of a 3.5-inch thickness of fiberglass batting is 10.9. Calculate the R value of a 3.5-inch thickness of still air, then discuss whether these two numbers are reasonable. (Hint: These reference values include the effects of convection.)
Does it ever make sense to say that one object is "twice as hot" as another? Does it matter whether one is referring to Celsius or Kelvin temperatures? Explain.
Calculate the rms speed of a nitrogen molecule at room temperature.
In Problem 1.16 you calculated the pressure of the earth鈥檚 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 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 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 1.16(b) to find a formula for in this case. The result should be a constant, independent of temperature and pressure, which evaluates to approximately . This fundamental meteorological quantity is known as the dry adiabatic lapse rate.
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