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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: 1st Law of Thermodynamics Chapter 10: Steady Flow Energy Equation Chapter 11: Heat Engines and Reversibility Chapter 12: 2nd Law of Thermodynamics Chapter 13: Entropy Chapter 14: General Energy Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering 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 cp and cv (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 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. Chapter 7: Ideal Gases & Associated Laws Khan Academy Chapter 7: Ideal Gases & Associated Laws THE IDEAL GAS EQUATION pv= RT or 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 P=pressure v=specific volume V=volume m=mass R=gas constant for a particular gas T=temperature in absolute units 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 Chapter 7: Ideal Gases & Associated Laws 1bar = 105 Pa Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws T2 = 20˚C = 273.15+20 = 293.15K Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws CONVERT To SI…N/m2 Chapter 7: Ideal Gases & Associated Laws Heat Capacity: amount of heat required to change the temperature of a substance by a given amount Joules Law: It is not dependent on pressure or volume. PV=mRT Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Both a function of Temperature Chapter 7: Ideal Gases & Associated Laws INTERNAL ENERGY AND ENTHALPY DIFFERENCES: Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws Mass x specific internal energy Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws Just calculated PV=mRT Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws For any process, change in internal energy: (U2- U1) = mCv(T2- T1) For any process, change in internal energy: (H2- H1) = mCp(T2- T1) 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 Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws IDEAL GAS PROCESSES Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws IDEAL GAS PROCESSES constant Upside down Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws IDEAL GAS PROCESSES Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws IDEAL GAS PROCESSES Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws Assume mass doesn’t change Adiabatic Process PV=RT H=U+PV (u2- u1) = Cv(T2- T1) Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering 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 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 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 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. V1/V2) and the work done on the air per unit mass. Next slide shows this Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Chapter 7: Ideal Gases & Associated Laws Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering 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. V1/V2) and the work done on the air per unit mass. Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering 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. V1/V2) and the work done on the air per unit mass. Dr. Joseph Stokes School of Mechanical & Manufacturing Engineering