MEDEP1T2 All Theory PDF

All Theory Combined in One Powerpoint Systems and control volumes Thermodynamics  all aspects of energy and energy transformation Closed system/control ground Open system/control volume Definition...

All Theory Combined in One Powerpoint Systems and control volumes Thermodynamics  all aspects of energy and energy transformation Closed system/control ground Open system/control volume Definition A system with constant mass A system or control volume with a mass flow through it Mass Does NOT cross system DOES cross system boundaries boundaries Energy (heat or DOES cross system boundaries DOES cross system work) boundaries Example 2 Properties of a system Description symbol Unit Pressure P Pa Pascal Temperature T K Kelvin Volume V m3 Cubic meters Specific volume v m3 / kg See density Density ρ kg / m3 Mass m kg Kilogram Specific heat c J/ kgK 3 Condition and equilibrium A state is determined by state variables, such as pressure, temperature, volume and mass. States can change (from state 1 to state 2) or be in equilibrium (state 1 or state 2). State variables in a State variables in a stationary homogeneous closed system: open system: depending on the time depending on the place 4 Processes and cycles Process: any change that a system undergoes from one state to another state (state change). Path: the 'way' that a system takes to get from one state to another state. Processes and cycles Process diagrams help visualize the process; Commonly used properties for coordinates are pressure P, temperature T and volume V; Properties are placed on the y- axis and x-axis of the process diagram. State diagram example: PV diagram 6 Processes and cycles A cycle is a sequence of processes, with the special condition that the system returns to its original state: 7 Forms of energy Important definitions Energy in Heat Work /formulas general Symbol E [J] Q [J] W [J] Specific energy/heat/work (per mass unit) Energy flow / heat flow / Power (per unit time) 𝟏 𝑱⁄𝒔 = 𝟏 𝑾 𝐸̇ = 𝑚̇ 𝑒 From 𝑊̇ , = 𝑚̇ 𝑤 , EP1T1.. 8 𝑊̇ , = 𝑚̇ 𝑤 , Forms of energy 𝑘𝑔 𝑚 𝑚 𝑚 𝑠 Mechanical energy is the form of energy that can be 𝑘𝑔 = 𝑠 directly converted into work by a mechanical device 𝑁 𝑚 𝑚 + 𝑠 𝑚 𝑁 𝑚. 𝑚 𝑚 + 𝑚 = + + 𝑘𝑔 − 𝑠 𝑘𝑔 𝑠 𝑠 Mechanical energy in a flowing fluid: 𝑚 [J/kg] Energy flow: [J/s] 9 Forms of energy Macro forms of energy, related to speed and external effects such as gravity. These are : kinetic energy (KE) potential energy (PE ) Micro forms of energy, related to the molecular structure of a substance and the degree of molecular activity (internal). Sum of all micro energy: internal energy (U) 10 Forms of energy (U) Internal energy (U): sum of all kinetic and potential energy of molecules. o Sensible energy/ Tangible energy (= related to temperature ) o Latent energy (= related to phase change ) o Chemical energy o Nuclear energy 11 Forms of energy – macro and micro Total Energy (E) Macro Micro Kinetic Potential Special one cases Internal Energy Energy : magnetic , electrical , Energy (U) (KE) (PE) surface tension energy 12 Forms of energy The total energy of a system consists of: - Internal energy U - Potential energy PE - Kinetic energy KE [J] - Total energy per unit mass (specific energy): [J/kg] 13 Energy transport by heat Heat (Q 1-2 = Q): form of energy transport between two systems (or a system and the environment) with temperature difference as the driving force. With a difference in temperature, energy transport takes place until thermal equilibrium is reached Heat flows from high to low temperature (T2>T1) 14 Specific Heat c – Material Property The amount of energy needed to increase the temperature of 1 kg of material by 1K Material Phase state Specific heat (in J/ kgK ) Aluminium Solid 880 Copper Solid 380 Water Liquid 4186 15 Water (ice) Solid (0°C) 2060 Energy transport through work Work (W 1-2 = W): form of energy transport across the system boundary, where temperature is not the driving force, and where force acts over a distance. E.g. a moving piston or a rotating shaft. No movement = no work! Unit of work: I. W 16 Work (W) in a process Work is determined by integration: The work is equal to the area under the curve in the PV diagram! 17 Work (W) in a process Work done by the gas depends on the process path Work done by the gas: expansion, W > 0 Work done on the gas: compression, W < 0 Net work during cycle: enclosed area 18 Energy transport – Heat and Work To make Energy Transfor possible: Heat and work happen at the boundary of the system Systems contain energy, but no heat or work Heat and work are only relevant in a process, not in a state Heat and Work have a quantity and a direction W > 0: Work delivered by the system to the outside Q > 0: Heat supplied to the system from the outside 19 First Law of Thermodynamics 1st law of thermodynamics: based on the law of conservation of energy. Energy cannot arise or disappear, but it can change form. 20 First Law of Thermodynamics Total energy change of a system : Without electrical, magnetic or surface tension effects, the total energy change is : For a stationary system the following applies : U  m( u 2  u1 ) KE  21 m( V2 2  V1 2 ) PE  mg( z 2  z1 ) 21 Total energy – closed systems Definition of closed system: a system with constant mass. Most closed systems remain stationary during a process, i.e. the speed and height of the center of gravity remain constant In that case : So, the change in total energy of a stationary system is equal to the change in internal energy ( Δ U) 22 Total energy – open systems / control volumes PE out Open system/control volume definition: KE out A system or control volume with a mass flow through it. The first law also applies here: g Q PE in KE in 23 Ideal gas law General gas law / Boyle and Gay Lussac 's law / universal gas law - An ideal gas is a non-existent concept, consisting of molecules that - collide elastically - have no mutual attraction - have no dimensions - The ideal gas law - provides a good approximation of the behavior of many known gases - describes the behavior of ideal gases under the influence of pressure , volume , temperature and number of particles - In EP1T2 we consider many issues as ideal gas! 24 §4.6 Ideal gas law 𝑃 𝑣=𝑅 𝑇 where: P press Pa 𝑣 specific volume m 3 /kg T temperature K R s specific gas constant J/ kgK Alternative formulas: 𝑃 𝑉=𝑛 𝑅 𝑇 𝑃 𝑉=𝑚 𝑅 𝑇 where: where: n number of moles [-] m mass kg R u universal gas constant V volume m 3 (R u = 8.314 kJ/ kmol·K ) R specific gas constant [J/ kg K ] 25 The ideal gas law – specific gas constant R s (Specific) gas constant is different for each type of gas. R s can be determined with: where: R u = Universal gas constant (R u =8.314 kJ/ kmol K ) M = Molar mass [kg/ kmol ] For values of R, see table A-2 ( p. 897) 26 Ideal gas law What's the benefit? 𝑃 𝑉 𝑃 𝑉=𝑚 𝑅 𝑇→ =𝑚 𝑅 𝑇 =constant The relationship between 2 states of an ideal gas with a fixed mass can be expressed by the following formula: 𝑃 𝑉 𝑃 𝑉 = 𝑇 𝑇 27 §5.1 Polytropic processes Polytropic process: the relationship between pressure P and Volume V holds: where: n: polytropic exponent (= constant) C: a constant 28 Polytropic processes Polytropic process: the relationship between pressure P and volume V holds: Whereby: n: polytropic exponent (= constant) C: a constant But… the ideal gas law then? 29 Polytropic processes – Poisson’s Laws Using the ideal gas law it can be deduced that: 30 Polytropic processes Process Condition n Example P- V diagram name Isobaric A process in n=0 which the pressure P remains constant Isochore A process in n=∞ which it volume V remains constant 31 Polytropic processes Process Condition n Example P- V diagram name Isothermal A process in n=1 which the temperature T remains constant Adiabatic No heat n= k (isentropic) exchange (Q) with the outside world 32 Ideal gases – specific heat relations Specific heat: General At constant pressure With the same volume Relationship between c p and c v for ideal gases: So: Specific heat ratio (k): For values of R, c p , c v and k, see table A-2 ( p. 897) 33 Work (W) in a process Work is determined by integration: The work is equal to the area under the curve in the PV diagram! 𝐴𝑟𝑒𝑎 = 𝑑𝐴 = 𝑃𝑑𝑉 34 Work (W) in a polytropic process For a polytropic state transition: 𝑃 𝑉 =𝐶 So: 𝐶 𝑃= =𝐶 𝑉 𝑉 Entering the integral for labor results in: 𝑉 −𝑉 𝐶 𝑉 𝑉 −𝐶 𝑉 𝑉 𝑃 𝑉 −𝑃 𝑉 𝑊 = 𝑃𝑑𝑉 = 𝐶 𝑉 𝑑𝑉 = 𝐶 = = −𝑛 + 1 −𝑛 + 1 1−𝑛 𝑷𝟐 𝑽𝟐 − 𝑷𝟏 𝑽𝟏 𝑾𝑩 = 𝟏−𝒏 35 Work (W) in special processes With a constant volume process (isochoric): V1 = V2 𝑊 = 𝑃𝑑𝑉 = 𝟎 36 Work (W) in special processes For a constant pressure process (isobaric): P1 = P2 𝑊 = 𝑃𝑑𝑉 = 𝑃 𝑉 − 𝑉 37 Work (W) in special processes At a constant temperature (isothermal): P1V1 = P2V2 𝑉 𝑊 = 𝑃𝑑𝑉 = 𝑃 𝑉 𝑙𝑛 𝑉 38 Heat (Q) in special processes Heat: the form of energy that is transferred between 2 systems or between a system and its environment, as a result of a temperature difference. Polytropic Q = heat [J] m = mass [kg] Adiabatic (Q=0) 𝑐 = 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 ℎ𝑒𝑎𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑜𝑙𝑦𝑡𝑟𝑜𝑝𝑖𝑐 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝐽⁄𝑘𝑔 𝐾 Isobaric (P=C) 𝒑 Or: c = 𝑐 − ∆𝑇 = 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑢𝑟𝑣𝑒𝑟𝑠𝑐ℎ𝑖𝑙 𝐾 Isochoric (V=C) 𝒗 Isothermal (T=C) c v specific heat at constant volume [J/ kg K ] c p specific heat at constant pressure [J/ kg K ] Specific heat is the energy (J) required to increase the temperature of a unit mass (kg) of a given substance by 1 degree (K). 39 (Special) polytropic changes of state State change Comparison Value Work Heat exponent Polytropic 𝑃𝑉 = 𝐶 𝑃 𝑉 −𝑃 𝑉 𝑄 = 𝑚 𝒄 ∆𝑇 𝑊 = 1−𝑛 Where: 𝑅 𝑛≠1 c=𝑐 − 𝑛−1 Adiabatic 𝑃𝑉 = 𝐶 n=k 𝑃 𝑉 −𝑃 𝑉 Q=0 𝑊 = 1−𝑘 Isobaric 𝑃𝑉 = 𝐶 n=0 𝑊 = 𝑃 ∗ (𝑉 − 𝑉 ) Q=m 𝑐 ∆𝑇 P = constant Isochore 𝑃𝑉 =𝐶 n =∞ 𝑊 =0 Q=m 𝑐 ∆𝑇 V = constant Isothermal 𝑃𝑉 = 𝐶 n=1 𝑉 𝑄=𝑊 T = constant 𝑊 = 𝑃𝑉 ∗ ln 𝑉 𝑉 = mRT ∗ ln 40 𝑉