Thermodynamics: Energy Conversion & Gas Laws

2. Chapter 4 • Thermodynamics is the science of energy conversion involving heat and other forms of energy, most notably mechanical work. It studies and interrelates the macroscopic variables, such as temperature, volume and pressure, which describe physical, thermodynamic systems. Meteorology \ Dr. Mazin sherzad

3. The Ideal Gas Law • An equation of state describes the relationship among pressure, temperature, and density of any material. • All gases are found to follow approximately the same equation of state, which is referred to as the “ideal gas law (equation)”. • Atmospheric gases, whether considered individually or as a mixture, obey the following ideal gas equation: gas equation:

4. Question: Calculate the density of water vapor which exerts a pressure of 9 mb at 20°C. Answer: Use the ideal gas law: Pv= ρRvT Pv = 9 mb = 900 Pa (a SI unit) Rv = R* / Mv = 461 J deg-1 kg-1 T = 273 + 20 (°C) = 293 K. So we know the density of water vapor is: ρ = Pv/ (RvT) = 900 / (461*293) = 6.67 x 10-3 kg m-3

5. VIRTUAL TEMPERATURE Moist air has a lower apparent molecular weight that dry air. The gas constant for 1 kg of moist air is larger than that for 1 kg of dry air. But the exact value of the gas constant of moist air would depend on the amount of water vapor contained in the air. It is inconvenient to calculate the gas constant for moist air. It is more convenient to retain the gas constant of dry air and use a fictitious temperature in the ideal gas equation. This fictitious temperature is called “virtual temperature”. This is the temperature that dry air must have in order to has the same density as the moist air at the same pressure. Since moist air is less dense that dry air, the virtual temperature is always greater than the actual temperature. actual temperature.

7. Laws of thermodynamics The four principles (referred to as "laws"): • The zeroth law of thermodynamics, which underlies the basic definition of temperature • The second law of thermodynamics, which states that the entropy of an isolated macroscopic system never decreases or (equivalently) that perpetual motion machines are impossible • The third law of thermodynamics, which concerns the entropy of a perfect crystal at absolute zero temperature, and which implies that it is impossible to cool a system all the way to exactly absolute zero. • The first law of thermodynamics, which mandates conservation of energy, and states in particular that the flow of heat is a form of energy transfer. Meteorology \ Dr. Mazin sherzad

8. Laws of thermodynamics Meteorology \ Dr. Mazin sherzad

9. The first law of thermodynamics, which mandates conservation of energy, and states in particular that the flow of heat is a form of energy transfer. TdS = Qthermal energy and pdV = W Therefore we can say dQ=dU+dW, where: U Internal energy (is the total energy contained by a thermodynamic system) (S) entropy (is a thermodynamic property that is a measure of the energy not available for work in a thermodynamic process)

10. Enthalpy • Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy The enthalpy of a system is defined as: H is the enthalpy of the system (in joules), U is the internal energy of the system (in joules), p is thepressure at the boundary of the system and its environment, (in pascals ) V is the volume of the system, (in cubic meters).

12. Consider a gas contained in a cylinder that is fitted with a piston: dW = Fdx When V1> V2 (the gas is compressed) work is done on the gas and W < 0 When V2> V1 (the gas expands) work is done by the gas and W > 0 The work done in going from volume V1to volume V2depends on the path of integration and as such is not an exact differential.

13. Specific heat: The ratio of the heat added to a system to the change in temperature of the systemdq/dTThe units for specific heat are J kg-1 K-1 In this case work is done by the gas, since as heat is added to the gas the gas expands (dW = pdV). Specific heat at constant volume (cv) At constant volume a gas does no work and the first lawof thermodynamics reduces to dq = du Specific heat at constant pressure (cp) Defined as:

14. Adiabatic process: dq= 0 For both processes V and α decrease For the isothermal process (shown by curve AB) this implies that p must increase For the adiabatic process (shown by curve AC) the internal energy, and thus temperature, increases. For the same mass of gas at the same volume (points B and C) the sample with the higher temperature (C) will also have a higher pressure, hence the adiabat (AC) on the p-V diagram is steeper than the isotherm (AB)

15. Specific Heat of Dry Air • For ordinary calculations value of cp = 1.0 kJ/kg.K (equal to kJ/kg.oC) -is normally accurate enough • For higher accuracy cp = 1.006 kJ/kg.K (equal to kJ/kg.oC) - is better

16. The value of cp and cv for dry air are: cp = 1004 J kg-1 K-1 cv = 717 J kg-1 K-1 Dry Adiabatic Lapse Rate • Consider an air parcel undergoing an adiabatic change in pressure, with no phase change of any water substance in the air parcel. For this air parcel the first law of thermodynamics can be written as: Combining these equations give: Since this change in pressure implies a change in elevation: From the hydrostatic equation : where p is the pressure, the density, g the acceleration of gravity, and Z the geometric height. Combining these equations give:

17. Dry and Moist Adiabatic Lapse Rates • Dry adiabatic lapse rate is constant = 10ºC/km. • Moist adiabatic lapse rate is NOT a constant. It depends on the temperature of saturated air parcel. • The higher the air temperature, the smaller the moist adiabatic lapse rate.

18. Example 3: 2 kg of ice at -10 oC and 3 kg of water at 70 oC are mixed in an insulated container. Find a) Equilibrium temperature of the system b) Entropy produced. Homework???