Lecture 2 - Thermodynamic Properties PDF

Thermofluids I: Thermodynamic “ENGN 2610” Lecture 2 Thermodynamic properties  Learning outcomes By the end of the lecture, you should gain the following outcomes: Understand the main thermodynamics properties:...

Thermofluids I: Thermodynamic “ENGN 2610” Lecture 2 Thermodynamic properties  Learning outcomes By the end of the lecture, you should gain the following outcomes: Understand the main thermodynamics properties: Textbook Chapter 1-5 to 1-10 ❑Density. ❑Pressure. ❑Temperature. 2  Density It is defined as mass per unit volume. For a differential volume element of mass dm and volume dV, density can be expressed as: 𝑑𝑚 𝜌= 𝑑𝑉 Remember the continuum assumption: properties of matter is distributed continuously throughout the substance. 𝜌𝑎𝑖𝑟 = 1.2 𝑘𝑔/m3 @ 1 atm 𝑀 and 20 C 𝜌= [𝑘𝑔/m3 ] 𝑉 𝜌𝑤𝑎𝑡𝑒𝑟 = 998 𝑘𝑔/m3 3  Density Density depends on pressure and temperature. For gases: 𝜌𝛼𝑃 𝜌 𝛼 1/𝑇 Air density @ 1atm 4  Density Specific volume [] 𝑉 1 𝜐 = = [𝑚3 /𝑘𝑔] Volume per unit mass 𝑚 𝜌 Specific gravity (Relative density) [S.G.]: Ratio of the density of a substance to the density of some standard substance at a specified temperature (usually water at 4°C, for which 𝜌𝑤 = 1000 𝑘𝑔/𝑚^3). 𝑆𝐺 = 𝜌/𝜌𝑤𝑎𝑡𝑒𝑟 Specific weight []: Weight of a unit volume of a substance. 𝛾 = 𝜌𝑔 [𝑁/𝑚3 ] 5  Pressure Pressure is the force exerted by a fluid on a unit area. Pressure results from the average effect of the forces produced on the container walls by the rapid and continual bombardment of the huge number of gas molecules. During collision, the molecules impart momentum on the walls. Pressure is the sum of the forces of all the molecules striking the walls per unit area of the wall. 𝐅 𝐏 = [𝐍/𝐦𝟐 ] Pressure acts 𝐀 on all directions 6  Pressure Atmospheric pressure 𝐅 compression 𝐏 = [𝐍/𝐦𝟐 ] 𝐀 Collision Momentum on walls Force Pressure 7  Pressure Atmospheric pressure: It is the weight exerted by the overhead atmosphere on a unit area of surface. 𝑃𝑎𝑡𝑚 = 1.013 ∗ 105 𝑁/𝑚2 Fluid pressure : vacuum 𝐹 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑 𝑐𝑜𝑙𝑢𝑚𝑛 𝑃= = 𝐴 𝐴 h 𝑃 = 𝑃𝑎𝑡𝑚 + 𝜌𝑔ℎ 𝑚𝑎𝑠𝑠 ∗ 𝑔 𝜌 ∗ 𝑉 ∗ 𝑔 𝑃= = = 𝜌𝑔ℎ a 𝐴 𝐴 8  Pressure Variation of Pressure with depth: 𝑃 = 𝜌𝑔ℎ = 𝛾ℎ The pressure of a fluid at rest increases with depth (as a result of added weight). h P 9  Pressure For fluids, whose density changes significantly with elevation: ෍ 𝐹𝑧 = 𝑚 𝑎𝑧 = 0 𝑃2 ∗ 𝑑𝑥 − 𝑃1 ∗ 𝑑𝑥 − 𝑊 = 0 𝑊 = 𝑚𝑔 = 𝜌𝑔𝑑𝑥𝑑𝑧 𝑃2 ∗ 𝑑𝑥 − 𝑃1 ∗ 𝑑𝑥 − 𝜌𝑔𝑑𝑥𝑑𝑧 = 0 d𝑃 = −𝜌𝑔𝑑𝑧 d𝑃 = −𝜌𝑔 𝑑𝑧 2 ∆𝑃 = − න 𝜌𝑔𝑑𝑧 Infinitesimal fluid element 1 10  Pressure SI Units 1 𝑃𝑎 = 1 𝑁/𝑚2 1 𝑎𝑡𝑚 = 1.013 ∗ 105 𝑃𝑎 = 1.013 𝑏𝑎𝑟 ≈ 1 𝑏𝑎𝑟 1 𝑘𝑃𝑎 = 1000 𝑃𝑎 1 𝑏𝑎𝑟 = 105 𝑃𝑎 = 100 𝑘𝑃𝑎 = 0.1 𝑀𝑃𝑎 ≈ 1 𝑎𝑡𝑚 Other Units 1 𝑘𝑔𝑓 Τ𝑐𝑚2 = 9.81 𝑁/𝑐𝑚2 = 9.81 ∗ 104 𝑁/𝑚2 1 𝑏𝑎𝑟 = 14.5 𝑝𝑠𝑖 11  Pressure Absolute vs. gage pressure: a 𝑷𝒈𝒂𝒈𝒆 𝐏𝐠𝐚𝐠𝐞 = 𝐏𝐚𝐛𝐬 − 𝐏𝐚𝐭𝐦 Atmospheric pressure 𝐏𝐯𝐚𝐜𝐮𝐮𝐦 = −𝑷𝒈𝒂𝒈𝒆 𝑷𝒂𝒃𝒔 𝑷𝒗𝒂𝒄𝒖𝒖𝒎 𝑷𝒂𝒕𝒎 b 𝐏𝐯𝐚𝐜𝐮𝐮𝐦 = 𝐏𝐚𝐭𝐦 − 𝐏𝐚𝐛𝐬 𝑷𝒂𝒃𝒔 Zero absolute pressure +𝑃𝑔𝑎𝑔𝑒 is used when 𝑃𝑎𝑏𝑠 > 𝑃𝑎𝑡𝑚. −𝑃𝑔𝑎𝑔𝑒 (𝑃_𝑣𝑎𝑐) is used when 𝑃𝑎𝑏𝑠 < 𝑃𝑎𝑡𝑚. 12  Pressure Manometers: ∆𝑃 = 𝜌𝑔∆𝑧 The manometer height is based on the pressure difference and the fluid density. For high P, use high density fluid. Ex: Mercury manometer 𝑃𝑔𝑎𝑠 = 𝑃1 = 𝑃2 = 𝜌𝑔ℎ + 𝑃𝑎𝑡𝑚  is the 𝑃𝑔𝑎𝑠 𝑔𝑎𝑔𝑒 = 𝜌𝑔ℎ manometer fluid 13  Pressure Manometers: ∆𝑃 = 𝜌𝑔∆𝑧 𝑃1 + 𝜌1 𝑔 𝑎 + ℎ = 𝑃𝐴 𝑃2 + 𝜌1 𝑔𝑎 + 𝜌2 𝑔ℎ = 𝑃𝐵 𝑃𝐴 = 𝑃𝐵 𝑃1 + 𝜌1 𝑔 𝑎 + ℎ = 𝑃2 + 𝜌1 𝑔𝑎 + 𝜌2 𝑔ℎ Another method: A relation between the pressure difference can be obtained by starting at point 1 with P1 moving along 𝑃1 − 𝑃2 = 𝜌2 − 𝜌1 𝑔ℎ the tube by adding or subtracting the (gh) terms 𝑖𝑓 𝜌1 ≪ 𝜌2 until we reach point 2 𝑃1 − 𝑃2 = 𝜌2 𝑔ℎ 𝑃1 + 𝜌1 𝑔 𝑎 + ℎ − 𝜌2 𝑔ℎ − 𝜌1 𝑔𝑎 = 𝑃2 14  Pressure Other pressure measuring devices: Pressure gages ❑What is the effect of temperature on pressure? 15  Pressure Problem 1: A manometer is used to measure the pressure in a tank. The fluid used has a specific gravity of 0.85, and the manometer column height is 55 cm. If the local atmospheric pressure is 96 kPa, determine the absolute pressure within the tank. 16  Pressure Problem 2: The water in a tank is pressurized by air, and the pressure is measured by a multifluid manometer. The tank is located on a mountain at an altitude of 1400 m where the atmospheric pressure is 85.6 kPa. Determine the air pressure in the tank if h1=0.1 m, h2=0.2 m, and h3=0.35 m. Take the densities of water, oil, and mercury to be 1000 kg/m3, 850 kg/m3, and 13,600 kg/m3, respectively. 17  Temperature What is temperature? Temperature as a measure of “hotness” or “coldness”. Heat is transferred from the body at higher temperature to the one at lower temperature until both bodies attain the same temperature. At that point, the heat transfer stops, and the two bodies are said to have reached thermal equilibrium. Zeroth law of thermodynamic: If two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. By replacing the third body with a thermometer, the zeroth law can be restated as two bodies are in thermal equilibrium if both have the same temperature reading even if they are not in contact. 18  Temperature Temperature scales: Celsius scale : On the Celsius scale, the ice and steam points were originally assigned the values of 0 and 100°C, respectively. Fahrenheit scale: The corresponding values on the Fahrenheit scale are 32° and 212°F. Kelvin Scale: -273 C is the absolute temperature: Lowest temperature that can be obtained at zero pressure. The thermodynamic temperature scale in the SI is the Kelvin scale. 19  Temperature Converting between scales: 𝑇 𝐾 = 𝑇 ℃ + 273.15 𝑇 𝑅 = 𝑇 ℉ + 459.67 𝑇 𝑅 = 1.8 ∗ 𝑇(𝐾) 𝑇 ℉ = 1.8 ∗ 𝑇 ℃ + 32 20  Summary At the end of this lecture, you should be able to answer the following questions: Define the density of a material and how it is affected by pressure and temperature. Define specific volume, specific gravity, and specific weight. What is the pressure and how it is calculated. Solve problems on the determination of the fluid pressure. Differentiate between absolute, gage, and vacuum pressure. Solve problems on measuring pressure using manometers. What is temperature? How to convert between different temperature scales? 21