Self-study questions – Ch. 2 & 3

Air parcels as thermodynamic systems

The following questions are drawn from pp. 49-51:

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1. In your own words, explain the concept of an air parcel.  What idealization(s) are employed?  Why is the concept of an air parcel useful? In what major way(s) does the idealization break down in the real world?

2. List the defining characteristics of open, closed, and isolated thermodynamic systems, and give examples of each.

3. When considering whether a system is open, closed, or isolated, why is it important to consider the time scale of interest?

4. Why is there no type of system corresponding to the special case that the system exchanges matter but not energy with its environment?

5. For each of the following things being treated as “the system,” state what the corresponding “environment” is. Also comment on whether (and when) it can be safely idealized as an open, closed, or isolated system.
a) A falling raindrop.
b) A parcel of air.
c) The planet Mars.
d) A tree.
e) An inflated party balloon.
f) A hurricane.

Working with system variables

The following questions are drawn from pp. 52-60:

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1. In your own words, explain the difference between a state variable and a process variable, and give your own examples of each (that are not the same as those mentioned on p. 52 or in Problem 2.2).

2. What is the meaning of a differential, and how big or small can one be? Why do they often occur in pairs in physical derivations?

3. In deriving physical relationships that start with differential equations, what mathematical step is almost always invoked so as to eliminate the differentials and obtain a function describing macroscopic changes?

4. When is it okay to have a differential quantity one side of an equation and a non-differential quantity on the other side?  Similarly, when is it okay to integrate one side of an equation but not the other?

5. Explain the difference between exact and inexact differentials.  What notation is used in the book to distinguish between the two? How are these related to the concept of state vs. process variables?

6. What property distinguishes each of the following?  a) an isothermal process.  b) an isobaric process.  c) an isochoric process.

7. From the following list, identify those variables that are extensive:  temperature, pressure, density, volume.  Convert the extensive variable(s) into an intensive form.

Experimental properties of gases

The following questions are drawn from pp. 61-70:

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1. The experimentally or theoretically derived relationship that ties together various physical properties of a particular substance (not necessarily a gas), such as density, temperature, and pressure, is called an                            .

2. A sample of a gas has a pressure of 1000 hPa and a temperature of 20\( ^\circ\)C, and a volume of 100 liters.  If the gas is then isothermally compressed to a new volume of 25 liters, what is the new pressure?  What experimental law discovered in the 1600’s predicts the new pressure?

3. The same sample of gas with the same initial conditions as above is heated isobarically to 100\(^\circ\)C.  What is its new volume?  What experimental law discovered in the late 1700’s predicts the new volume?

4. Three bottles contain three different gases —  helium, nitrogen, and argon — at the same temperature, pressure, and volume. In addition to those three variables, what physical property do all three gas samples have in common?

5. Combining Boyle’s Law, Charles’ Law, and Avogadro’s Law into one single equation leads to what important equation of state for gases?

6. Under some circumstances, the Ideal Gas Law isn’t sufficiently accurate in describing the equation of state of real gases.  What is the name of a more accurate equation of state for gases, and what two non-ideal properties does it take into account?

7. The original form of the Ideal Gas Law describes the relationship between the pressure, the volume, the temperature, the number of moles of a gas, and a Universal Gas Constant.  The meteorological form of the IGL that we will use differs in what ways, and why?

8. A sealed one-liter container holds nitrogen at a pressure of 200 hPa.  Another sealed two-liter container holds oxygen at a pressure of 100 hPa.  Both are at the same temperature.  If the contents of both containers are then pumped into a third (previously evacuated) container with a volume of four liters, what will be partial pressures of each gas?  What will be the combined pressure?

9. The gas constant R used in the meteorological form of the IGL depends on what property of the gas in question?  How does one compute R for a particular mixture of different gases?

Equation of state for moist air

The following questions are drawn from pp. 71-78:

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1. Give the form of the Ideal Gas Law appropriate to pure water vapor.

2. Know the definitions, standard units, and physical meaning of the following variables relating to the moisture content of air:
a) absolute humidity
b) vapor presure
c) mixing ratio
d) specific humidity
e) virtual temperature

3. Give the approximate formula we will generally use for the relationship between mixing ratio, specific humidity, vapor pressure, and total air pressure.  According to this approximate relationship, what is the numerical difference between mixing ratio and specific humidity?

4. Write down, and know how to use, the “convenient” (simplified) expression for virtual temperature that we will generally use for problems requiring virtual temperature.

5. Write down two equivalent versions of the IGL that are applicable to moist air (air for which the water vapor content is non-zero).

6. Be able to explain to a non-meteorologist what virtual temperature is.

7. Be able to perform IGL calculations for arbitrary combinations of humidity, density, pressure, vapor pressure, mixing ratio, temperature, and/or virtual temperature.

8. Under what circumstances can we often ignore the distinction between real temperature and virtual temperature? When should we not ignore it?

Buoyancy

The following questions are drawn from pp. 78-81:

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1. Given suitable information about mass, volume, and/or density, be able to compute the net buoyant force on any object that is immersed in a fluid.

2. A balloon filled with helium and carrying a payload is allowed to rise through the atmosphere. Assuming the balloon is sturdy enough to not burst, what determines the maximum altitude to which the balloon can rise? In other words, what property of the atmosphere at any given level are you comparing with what net property of the balloon + payload?

3. A parcel of air has a temperature of 20.0\( ^\circ\)C and a specific humidity q of 15 g/kg. The surrounding atmosphere has a temperature of 21.0\( ^\circ\)C and a specific humidity q of 5 g/kg.
a) Determine whether the parcel will rise, sink, or remain at its initial position.
b) Determine its rate of vertical acceleration, ignoring other forces.