Adobe Systems Professor Vojtěch Mornstein, Dept. Of Biophysics, Medical Faculty MU 1 The Foundation Course on Physics The Thermodynamic Processes Image result for locomotive gif See also Glencoe pp. 318 – 355, 368-371 Adobe Systems Back to Ideal Gas Law ̶Ideal gas law: ̶The state parameters (quantities which values determine/describe a thermodynamic state) are interrelated by the state equations. ̶The simplest state equation: the ideal gas law (= state equation of ideal gas), which can be written in different ways, e.g.: ̶ ̶ (for constant amount of substance n – this value becomes a component of the constant) , ̶where p is the gas pressure given in pascals [Pa], V is the volume of the gas [m3], T is the Kelvin temperature* [K], R the molar or universal gas constant (= 8.31 J·K-1·mol-1), and n is amount of substance in moles [mol]. *Kelvin temperature = absolute temperature = thermodynamic temperature Adobe Systems Normal values of p and T ̶For many calculations in thermodynamics, it is necessary to know what are the values of normal molar volume Vn, normal pressure pn and normal temperature Tn: ̶pn = 1.01325×105 Pa = 101,325 kPa = 1013,25 hPa ≈ 1 atm ̶Tn = 273.15 K* (0 °C) ̶Vn = 22.4×10-3 m3mol-1 = 22.4 litres ̶ ̶(Note: All gases have the same molar volume at the same temperature and pressure!!!!!) Normal molar volume is a volume occupied by one mole of perfect gas at normal pressure pn and temperature Tn. Based on the equation of ideal gas law, it is possible to derive** simply other laws which are applicable only under some specific conditions. Processes correctly described by these laws are reversible and can be presented as curves of a typical shape in a pV-diagram (see below). ̶ *It can be also 293.15 K, but it will cause a little increase in the molar volume. **The scientific historical development was different! Adobe Systems Thermodynamic processes a) Boyle's law (Boyle – Mariotte law): During an isothermal process, temperature T has a constant value (does not change). Value of temperature is included in the constant as shown below. p1·V1 = p2·V2 = const. A gas is slowly compressed (or expanded) and the heat can be transferred to/from the surrounding: like slowly inflating a rubber balloon, bubbles ascending in water ….. Výsledek obrázku pro isothermal process animation Relevance: In homoeothermic organisms most processes take place at about constant temperature! Adobe Systems Thermodynamic processes ̶b) Gay-Lussac's law: ̶Pressure p is constant – an isobaric process takes place. Value of pressure is included in the constant: ̶ Výsledek obrázku pro isobar process The weight W exerts always the same force on the gas under the movable piston. Volume and temperature are changing but pressure is constant A gas is slowly heated and its volume increases at a constant pressure: most processes around us take place under constant pressure… like in the most living organisms!!! Adobe Systems Thermodynamic processes ̶c) Charles's law: Volume V is constant – an isochoric (i.e. isosteric) process takes place. Value of volume is included in the constant: ̶ A system consisting of water and water vapour is slowly heated and its volume is kept constant: cooking in a pressure cooker ….. autoclave used for sterilization in labs is similar. Výsledek obrázku pro isochoric process The piston does not move, pressure and temperature increase. Adobe Systems Pressure cooker and Autoclave Výsledek obrázku pro autoclave Výsledek obrázku pro autoclave Výsledek obrázku pro pressure cooker kitchen Small lab industry Adobe Systems Thermodynamic processes ̶A special case – adiabatic process. The system is thermally insulated. In the following equation the k (kappa) is the Poisson constant which has different values for different gases (given mainly by number of atoms in their molecules). ̶ p·Vk = const. In real conditions, adiabatic-like processes are fast enough to avoid heat exchange with surroundings. adiabatic.png Only internal energy U can be transformed into useful work W! Thermal insulation Adobe Systems p-V diagram The pV-diagram is the frequently used graphic representation of the reversible thermodynamic processes (see also the slide about the isothermal process!). What is the meaning of any single point in a p-V diagram? For an ideal gas and n = const., this point represents a single thermodynamic state! A reversible TMD process can be represented by a line (point by point = state by state) !!! For example: Obsah obrázku text, diagram, snímek obrazovky, řada/pruh Popis byl vytvořen automaticky Adobe Systems pV - diagram ̶Different thermodynamic processes are represented by different shapes of p(V) function – it means they have different pV-diagrams. ̶ ̶ ̶ ̶1 – isothermal process, The line is an isotherm ̶2 – isobaric process, The line is an isobar ̶3 – isochoric* process The line is an isochore ̶4 – adiabatic (also isoentropic**) process. The line is an adiabat, steeper compared with an isotherm ̶ tmd%20processes *called also isovolumetric or isosteric **entropy – see next lecture Adobe Systems Thermodynamic systems can do some work! (but they need energy to do it) Image result for work in physics joke More in the next lecture! Adobe Systems Work done in TMD processes ̶1 – isothermal ̶ ̶2 – isobaric ̶ ̶3 – isochoric ̶ ̶4 – adiabatic process ̶ ̶ Work done is always equal to the area below the p(V) curve! It can be seen best in case of isobaric process. Výsledek obrázku pro isobaric work The differences are substantial!!! Adobe Systems Heat and Heat Capacity We know already: Heat energy Q is the energy related to thermal motion of molecules*. It is interchanged between thermodynamic systems during thermodynamic processes. The thermal motion is chaotic movement of particles which move randomly in all possible directions. Vector sum of vectors of their velocities would be equal to zero (which is not so when we summarise or average absolute values of particle velocities or their second powers). The unit of heat energy is joule [J]. An often-used old unit of heat, the calorie** (amount of the heat necessary for heating 1 g of water by 1 oC) is: 1 cal (calorie) = 4.186 J British thermal unit 1 BTU = 1 055,05585 J (In Czechia, BTU is almost unknown) ̶ *Heat can be interchanged also in the form of electromagnetic radiation **Calories used for description of energetic content of the food are commonly the so-called big calories (kilocalories) Adobe Systems Heat and Heat Capacity Heat capacity. Heat interchange can cause a change of body temperature. Heat capacity K of a body is the amount of heat causing its temperature increase by 1 oC. We can write: Q = K·ΔT ̶ Specific heat capacity C is the heat capacity of unit mass of a substance: ̶ Q = C·m·ΔT, ̶ where C is given in [J·kg-1·K-1], m is mass of substance [kg], ΔT is the temperature change [K], and Q – heat interchanged [J]. C depends on the kind of thermodynamic process. Cp – heat capacity measured in an isobaric process (at constant pressure) – is greater than Cv – heat capacity measured in an isochoric process (at constant volume). In the first case it can be explained by doing work, which consumed a part of absorbed heat. In the second case (Cv) no work can be done because the “piston” cannot move (DV = 0). ̶ Adobe Systems Some specific heat capacities unit 5 second graf Huge amount of heat can be stored in the seas – it stabilises temperature of Earth surface!!!!! Adobe Systems Calorimetry The „system“ interchanges heat with the water bath: http://chemlab.truman.edu/CHEM130Labs/CalorimetryFiles/CalFig1.gif DQw = DQS mwCw(Tf – Tw) = mSCS(TS – Tf), Where mw is mass of water, Cw is specific heat capacity of water, Tf is final temperature of water+system, Tw is initial temperature of water, mS is mass of the „system“, CS is specific heat capacity of the „system“, TS is initial temperature of the „system“ . To obtain correct results of calculations we have to consider also the heat capacity of the calorimeter itself! Adobe Systems Thermal conductivity ̶Equation of thermal conduction. A steady heat conduction can be easily illustrated by a rod (cylinder) of a length d, one end of which is kept at the temperature t1 and the second one at the temperature t2. The temperature difference Dt = t2 - t1 is constant, the temperature decreases uniformly from the warmer end to the colder one. The fraction Dt/d denotes the temperature gradient. Amount of heat Q which passes through the rod in an arbitrary (normally oriented) cross-section A during time t is: ̶ ̶ ̶ ̶The proportionality constant l is the coefficient of thermal conductivity. By the magnitude of this coefficient, we can distinguish good and poor thermal conductors – the second ones are called thermal insulators. Water belongs among relatively good heat conductors, even better are the metals. Typical thermal insulators are e.g. glass, plastics, porous materials, feathers, textile, glass wool etc. ̶ Adobe Systems Thermal conductivity Výsledek obrázku pro thermal conductivity Heat flux in a metallic rod. Is it (could it be) a steady flux? Discuss the problem. Consider the ambient medium. Adobe Systems Thermal conductivity ̶The above equation of heat conduction is the simplest mathematical representation of the problem which otherwise has to be solved by means of integration of differential equations. ̶Thermal resistance R characterises thermally insulating properties of a material layer of given thickness. If we know the value of the coefficient of thermal conductivity of the material layer, and the heat is transmitted uniformly and normally to the material layer, the thermal resistance is defined as R = d/l, where d is the layer thickness [m] and λ [W·m-1·K-1] is the coefficient of thermal conductivity. ̶ Adobe Systems Thermal conductivity Výsledek obrázku pro thermal conductivity table Výsledek obrázku pro thermal conductivity table There are some differences / how to explain them? How to explain apparent difference between the diamond and the air? Adobe Systems Thermal expansion of liquids and solids Thermal expansion: Changes in temperature lead to expansion or contraction of solids and liquids. In most cases, the dimensions of a body increase with temperature. Thermal linear expansion will be explained first: Δl = α·l0·ΔT i.e. l = l0 + α·l0·ΔT [m], where Δl = l – l0 is the linear (longitudinal) expansion [m], ΔT is the temperature increase [K or oC], l0 is the initial length of the body, and α is the coefficient of linear expansion (called also linear thermal expansivity). ̶ Adobe Systems Thermal expansion of liquids and solids Thermal volume expansion can be expressed in the following way: ΔV = b·V0·ΔT i.e. V = V0 + b·V0·ΔT b is coefficient of volume expansion. It can be approximated: V ≈ V0 + 3α·V0·ΔT (b ≈ 3a) ̶ Material a coefficient [°C-1] Dl per 1 m and DT 100 °C b coefficient [°C-1] DV per 1 litre and DT 100 °C aluminium 23Í10-6 2.3 mm 69Í10-6 6,9 ml Bottle glass 9Í10-6 0.9 mm 27Í10-6 2,7 ml Cooking glas 3Í10-6 0.3 mm 9Í10-6 0,9 ml Concrete 12Í10-6 1.2 mm 36Í10-6 3,6 ml copper 17Í10-6 1.7 mm 51Í10-6 5,1 ml methanol ----------- --------- 1200Í10-6 120 ml gasoline ----------- --------- 950Í10-6 95 ml water ----------- --------- 210Í10-6 21 ml Adobe Systems Thermal expansion of liquids and solids ̶Applications and examples: Výsledek obrázku pro rail gaps https://upload.wikimedia.org/wikipedia/commons/a/a1/Spoorspatting_Landgraaf.jpg It can happen in very hot days! Výsledek obrázku pro thermometer Související obrázek Adobe Systems Thermal expansion of liquids and solids Výsledek obrázku pro thermal expansion pipes Výsledek obrázku pro thermal expansion Výsledek obrázku pro thermal expansion Expansion loops and joints Adobe Systems The end Version December 2024