EAS 6140 Thermodynamics

Worksheet 7– Combined 1st and 2nd Law

14. Write the first and second law combined in enthalpy form (intensive)

15. The Gibbs energy is defined as g = u - T pv

Write an expression for the Gibbs energy in differential form

16. Using the expressions in #14 and #15, write an expression for the Gibbs energy in differential form that has natural independent variables T, p.

12. Write the natural independent variables for:

internal energy:entropy and volume

enthalpy:entropy and pressure

Gibbs function:temperature and pressure

13. The conditions for thermodynamic equilibrium are:

a) at constant T and p:dg = 0

b) at constant  and p:dh = 0

c) at constant  and V:du = 0

17. Match the thermodynamic equilibrium conditions:

___c_____ constant , va. dg = 0

___b_____ constant , pb. dh = 0

___a_____ constant T, pc. du = 0

Potential temperature and the second law

We previously derived equation (2.22):

12. Which of the following equations were used in this derivation (circle all that apply)

a) first law of thermodynamics

b) second law of thermodynamics

c) ideal gas law

d) hydrostatic equation

13. Which of the following assumptions were made in this derivation (circle all that apply)

a) adiabatic

b) isothermal

c) isobaric

d) reversible

The potential temperature, , for the atmosphere is defined as

where po is 1000 hPa (mb). The potential temperature may be looked upon as the temperature of a sample of gas would have if it were compressed (or expanded adiabatically from a given state p and T to a reference pressure of 1000 hPa (mb). Refer to p 66.

14. Take the log of the potential energy equation, then write in differential form (i.e. in the left hand side you will have d(ln)

15. Write the first and second law combined in enthalpy form for an ideal gas (2.3.2)

16. From the expressions in #14 and #15, write an expression that relates entropy to potential temperature.

17. If potential temperature remains constant, the entropy (increases, decreases, remains the same).

Remains the same

18. The potential temperature remains constant for a sample of ideal gas under dry adiabatic ascent/descent (yes, no, sometimes)

Yes

19. The potential temperature of a parcel of air with T=288 K at p=900 hPa (mb) is

(greater than, less than, equal to) 288 K.

Greater than

EAS 6140 Thermodynamics of Atmospheres and Oceans

Thermodynamic Charts

Important Note – Because in viewing these charts you might see a slightly different value, this could lead to differences in calculation results. So use the numbers here in a relative comparison to your findings.

Using the Stuve (or Skew-T) diagram, read off the temperature and determine the potential temperature at each of the following levels

LevelTFFR soundingOAK sounding

T T

1000 mb27 30020293

900 mb20 30222302.12

700 mb10 313.49312.28

500 mb-7 324.32-9321.88

Estimate dT/dz and d/dz for the following layers

Level TFFR soundingOAK sounding

T T

1000-900 mb-10.2ºC/km 2.9ºC/km+3.0075ºC/km13.7 ºC/km

700-500 mb-6.28ºC/km 4.04ºC/km-6.69ºC/km 3.56ºC/km

Determine the change in T and  of an air parcel initially at 900 mb if subjected to

TFFR soundingOAK sounding

T T

a. adiabatic lifting of 100 mb-100-100

b. adiabatic lowering of 100 mb+100+100

c. radiative heating of 10oC+10+10+10+10

d. radiative cooling of 10oC-10-10-10-10

Sketch the following paths on the TFFR diagram

a) A parcel of air is lifted dry adiabatically from an initial height of 900 mb to a height of 700 mb. The parcel is then lowered back down to the initial pressure. Label this path A. Is this path reversible? yes

b) A parcel of air is lifted dry adiabatically from an initial height of 900 mb to a height of 700 mb. The parcel is then heated radiatively by 10oC at constant pressure. The parcel is then lowered back down to the initial pressure.Label this path B. Is this path reversible?no