Download 9. Entropy 2nd and 3rd laws/ Thermodynamic processes / Droplet

Prof. Dr. J.P. Burrows
Institute of Environmental Physics
Atmospheric Physics, WS 2007/2008
Exercise 9
9.1 Entropy in second and third laws of thermodynamics
(2pts) 1. Explain the statistical definition of entropy
(4pts) 2. Consider a “thermodynamic system” of two dices and let the energy of a certain throw
(state of the system) be the sum of the two values of the dices. Calculate the respective
entropy for all possible states (1), (2), (3),. . . . . . .,(11),(12).
(3pts) 3. Both in words and equations. Describe the following and explain all occurring variables:
(a) thermodynamic definition of entropy
(b) the second and third law of thermodynamics (state both laws in terms of entropy).
(6pts) 4. Determine the following consequences of third law. Justify your answer using partial
differentials of entropy with respect to thermodynamic variables pressure p, volume V ,
temperature T .
As T → 0, what happens to (a) the value of heat capacity (b) thermal expansion (c) ideal
gases
9.2 Thermodynamic processes, Internal energy and entropy
If an n mole ideal gas with the initial temperature T0 , and volume V0 first expands quasistatically
and isothermally to the volume V1 , then expands quasi-statically and adiabatically to the volume
V2 , and finally is compressed quasi-statically and isobaricaly back to the volume V0 . For an ideal
gas, the heat capacity Cv and the ratio of specific heats γ are constants.
(3pts) 1. Sketch these three stages in a P -V diagram.
(8pts) 2. Calculate the net change in internal energy, ∆U, from the initial to the final state.
(5pts) 3. Calculate the net change in entropy, ∆S, from the initial to the final state.
9.3 Radiation budget
(2pts) 1. Explain the term of radiative forcing. The following figure roughly shows the annually
and longitudinally averaged energy received and emitted in different latitudes.
Radiation received
Radiation emitted
North pole
Equator
South pole
(2pts) 2. Is the imbalance at nearly all latitudes a contradiction to the conservation of energy and
the fact that Earth is in radiative equilibrium with the ambient space? Explain why this
distribution is important for atmospheric circulation.
9.4 Water: in ocean, droplet growth, and phase diagram
Assume a globally constant initial temperature of 15◦ C,
(2pts) 1. Calculate the energy needed to evaporate all water of the oceans. The total mass of the
oceans on Earth is 1.4 · 1021 kg.
(2pts) 2. Assume that all water has evaporated and that the temperature for the whole atmosphere
is constant at 5◦ C. If all water vapour condenses out, what would be the increase in air
temperature? Use the total mass of the atmosphere is 5 · 1018 kg.
(2pts) 3. Explain different types (condensation, accretion) of droplet growth. Which role is played
by the size of the particle?
(2pts) 4. Consider the phase diagram of water. Explain why an ice skater skates easily. Hint: consider the transition line between the solid and the liquid state.
9.5 Tropospheric and stratospheric temperatures
Temperatures of the lower stratosphere have been monitored by a number of instruments (see
figure below). These observations show a cooling of the lower stratosphere by about 0.5 K per
decade.
(3pts) 1. Why does an enhanced CO2 concentration in the lower troposphere lead to a cooling of
the upper troposphere and lower stratosphere?
(3pts) 2. What about O3 ? How do changes in the amount of ozone affect the temperature of the
stratosphere?
(4pts) 3. How do volcanic eruptions effect the lower stratosphere? Why is a short-term increase in
temperature observed after each major volcanic eruption event?
Return date: Monday, 28. Jan. 2008, 17:00, Post Box 100
Tutor: Joseph Pagaran, Room: S4300, Tel. No.: 0421-218-8265, email: [email protected]
Additional info: http://www.iup.uni-bremen.de/~ pagaran/AP0708.html