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?
Fahrenheit freezing point of water = 32
Fahrenheit boiling point of water = 212
212 - 32 = 180 between the freezing point and boiling point of water.
Celsius freezing point of water = 0
Celsius boiling point of water = 100
100 - 0 = 100 between the freezing point and boiling point of water.
The ratio for Celsius to Fahrenheit of and the ratio of Fahrenheit to Celsius of
then 32 = 0
Hence the formula for degree Celsius to Fahrenheit is localid="1649151785065"
Absolute zero = 0K
K - 273.15 =
= 0 - 273.15 = -273.15
we know that
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.
Pretend that you live in the th century and don't know the value of Avogadro's number* (or of Boltzmann's constant or of the mass or size of any molecule). Show how you could make a rough estimate of Avogadro's number from a measurement of the thermal conductivity of gas, together with other measurements that are relatively easy.
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