1. Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Summary of Energy Topics Chapter 1: Thermodynamics / Energy Introduction Chapter 2: Systems & Processes Chapter 3: Work, Energy, Temperature & Heat Chapter 4: Work Processes of Closed Systems Chapter 5: Thermodynamic Properties Chapter 6: Steam Tables Chapter 7: Ideal Gases Chapter 8: Conservation of Mass & Energy Chapter 9: 1 st Law of Thermodynamics Chapter 10: Steady Flow Energy Equation Chapter 11: Heat Engines and Reversibility Chapter 12: 2 nd Law of Thermodynamics Chapter 13: Entropy Chapter 14: General Energy

2. Chapter 7: Ideal Gases & Associated Laws We have steam tables for water, but what about other gases? Ideal gases uses a simple equation to describe a gas over a wide range of its possible thermodynamic states Assumes that the specific heats c p and c v (specific heat capacity at constant pressure and volume respectively) are constant, thus changes in specific internal energy u or the specific enthalpy h can be calculated without thermodynamic tables. Most gases, such as air or hydrogen, can be regarded as 'ideal gases' like at: –temperatures well above their respective critical temperatures –pressures well below their respective critical pressures. –at very low pressures

3. Chapter 7: Ideal Gases & Associated Laws Ideal Gases: Do not attract or repel each other At normal temperatures and pressures most gases act similar to ideal gases.

4. Chapter 7: Ideal Gases & Associated Laws Khan Academy

5. Chapter 7: Ideal Gases & Associated Laws THE IDEAL GAS EQUATION pv= RTor pV=mRT where R is known as the specific gas constant (dry air R = 286.9 J /kg.K) R depends only on the molar mass of the gas, i.e. Specific Gas Constant: where is known as the universal gas constant (= 8.3145 kJ/kmol.K). The molar mass, has the units of kg/kmol. Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering P=pressure v=specific volume V=volume m=mass R=gas constant for a particular gas T=temperature in absolute units

6. Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering 1bar = 10 5 Pa

7. Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering T 2 = 20˚C = 273.15+20 = 293.15K

8. Chapter 7: Ideal Gases & Associated Laws CONVERT To SI…N/m 2

9. Chapter 7: Ideal Gases & Associated Laws Joules Law: Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Heat Capacity: amount of heat required to change the temperature of a substance by a given amount It is not dependent on pressure or volume. PV=mRT Both a function of Temperature

10. Chapter 7: Ideal Gases & Associated Laws INTERNAL ENERGY AND ENTHALPY DIFFERENCES: Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

11. Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

12. Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

13. Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Mass x specific internal energy

14. Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Just calculated PV=mRT

15. Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

16. Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering The heat energy required to raise the temperature of mass m from t1 to t2 at constant volume The heat energy required to raise the temperature of mass m from t1 to t2 at constant pressure For any process, change in internal energy: (U 2 - U 1 ) = mCv(T 2 - T 1 ) For any process, change in internal energy: (H 2 - H 1 ) = mCp(T 2 - T 1 )

17. Chapter 7: Ideal Gases & Associated Laws IDEAL GAS PROCESSES Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

18. Chapter 7: Ideal Gases & Associated Laws IDEAL GAS PROCESSES Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering constant Upside down

19. Chapter 7: Ideal Gases & Associated Laws IDEAL GAS PROCESSES Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

20. Chapter 7: Ideal Gases & Associated Laws IDEAL GAS PROCESSES Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

21. Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering H=U+PV (u 2 - u 1 ) = Cv(T 2 - T 1 ) PV=RT Assume mass doesn’t change  Adiabatic Process

22. Chapter 7: Ideal Gases & Associated Laws EXAMPLE : Adiabatic compression A common example of adiabatic compression is the compression stroke in a petrol engine. Calculate the temperature of the compressed gas in the engine cylinder under the following conditions: that the uncompressed volume of the cylinder is 1 litre, that the gas within is nearly pure nitrogen (thus a diatomic gas with five degrees of freedom; so γ = 7/5), and that the compression ratio of the engine is 10:1 (that is, the 1 litre volume of uncompressed gas will compress down to 0.1 litre when the piston goes from bottom to top. The uncompressed gas is at approximately 300 K, and a pressure of 1 bar or 0.1MPa (100,000 Pa), (typical sea-level atmospheric pressure). Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

23. Chapter 7: Ideal Gases & Associated Laws EXAMPLE : Adiabatic compression A common example of adiabatic compression is the compression stroke in a petrol engine. Calculate the temperature of the compressed gas in the engine cylinder under the following conditions: that the uncompressed volume of the cylinder is 1 litre, that the gas within is nearly pure nitrogen (thus a diatomic gas with five degrees of freedom; so γ = 7/5), and that the compression ratio of the engine is 10:1 (that is, the 1 litre volume of uncompressed gas will compress down to 0.1 litre when the piston goes from bottom to top. The uncompressed gas is at approximately 300 K, and a pressure of 1 bar or 0.1MPa (100,000 Pa), (typical sea-level atmospheric pressure). Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

24. Chapter 7: Ideal Gases & Associated Laws EXAMPLE : Adiabatic compression A common example of adiabatic compression is the compression stroke in a petrol engine. Calculate the temperature of the compressed gas in the engine cylinder under the following conditions: that the uncompressed volume of the cylinder is 1 litre, that the gas within is nearly pure nitrogen (thus a diatomic gas with five degrees of freedom; so γ = 7/5), and that the compression ratio of the engine is 10:1 (that is, the 1 litre volume of uncompressed gas will compress down to 0.1 litre when the piston goes from bottom to top. The uncompressed gas is at approximately 300 K, and a pressure of 1 bar or 0.1MPa (100,000 Pa), (typical sea-level atmospheric pressure). Dr. Joseph Stokes School of Mechanical & Manufacturing Engineering

25. Chapter 7: Ideal Gases & Associated Laws EXAMPLE Air at 1 bar and 20°C in a closed cylinder is compressed adiabatically in an equilibrium process to 5 bar, in order to pump up a dinghy. Determine the final temperature in °C, the compression ratio (i.e. V 1 /V 2 ) and the work done on the air per unit mass. Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Next slide shows this

26. Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

27. Chapter 7: Ideal Gases & Associated Laws EXAMPLE Air at 1 bar and 20°C in a closed cylinder is compressed adiabatically in an equilibrium process to 5 bar, in order to pump up a dinghy. Determine the final temperature in °C, the compression ratio (i.e. V 1 /V 2 ) and the work done on the air per unit mass. Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

28. Chapter 7: Ideal Gases & Associated Laws EXAMPLE Air at 1 bar and 20°C in a closed cylinder is compressed adiabatically in an equilibrium process to 5 bar, in order to pump up a dinghy. Determine the final temperature in °C, the compression ratio (i.e. V 1 /V 2 ) and the work done on the air per unit mass. Dr. Joseph Stokes School of Mechanical & Manufacturing Engineering