Tiêu đề BME Chap - 3.pdf ✅

(Properties of GasesPage no. (3-3 Basic Mechanical Engineering (GTU-FY-Common) 3.3 CHARLE'S LAW 3.1 INTRODuCTION UQ. State and Explain Charles's law. An ideal or perfect (GTU Summer 2014 gas is a state of a substance whose evaporation from the liquid state is complete. Perfect gas obeys the gas laws under all conditions of temperature and pressure. No gas is perfect but real gases which are difficult to liquefy such as oxygen, hydrogen, air etc. within certain temperature limits may be considered as perfect gases. Statement: It states, "The volume of a given mass ofa perfect gas varies directly as its absolute temperature when the absolute pressure remains constant. VoT (when p is constant) A vapour is a state of substance whose evaporation from its liquid state is partial. It contains liquid particles in suspension e.g. steam. With change in temperature and pressure the state of vapour changes by evaporation and condensation hence the vapour do no obey gas laws. However, superheated vapour approximately behaves like a perfect gas V or T constant The behaviour of perfect gas is governed by gas laws which have been established from experimental results. These laws are (i) Boyle's law (i) Charle's law (ii) Gay-Lussac law iV2 V 3.2 BOYLE'S LAW V Volume Fig. 3.2.2: Charles law State Boyle's law. GTU-Winter 2016) As shown in Fig. 3.2.2. if vj and Ti are initial pressure and temperature t point I and v and T> are final pressure OStatement : It states, "The volume of a given mass of a and perfect gas varies inversely as its absolute pressure, when the temperature remains constanf". temperature at point 2, then for different state points, = Constant VCp (when T is constant) PV = constant 3.4 or GAY-LUSSAC LAW As shown in Fig. 3.2.1, let a quantity of gas at pressure pj and volume v change its pressure and volume in cylinder without Statement : It states, "The absolute pressure of a given mass change in temperature. Let P2 and V2 are respective final pressure and volume after the end of expansion of gas. of perfect gas varies directly as its absolute temperature when the volume remains constant. For different state points, T (when v is constant) For different state points, Pi V P2 V2=Constant PA = constant 1 3.5 AVOGADRO'S LAW Ua. State Avogadro law. ----- GTU Winter 2016) P --~* ---*- Statement : It states, "Equal volumes of all gases at the sanie temperature and pressure contain equal number molecules." of Let m = Mass of gas Fig. 3.2.1: Boyle's law M = Molecular mass of gas n = Number of moles (New Syllabus w.e.f academic year 18-19) (G12-06) Tech-Neo Publications...A SACHIN SHAH Venu Jre
Basic Mechanical Engineering (GTU-FY-Common) (Properties of Gases) ..Page no. (3-4) m = Mxn .It also states that volume of a gas at NTP (Normal Temperature and Pressure) whose mass is equal to its kg mole is 22.4 m. The volume occupied by I mole of any gas at NTP Let a given mass ( m = I kg) of a perfect gas expands from state I with pressure P, volume vj and temperature T1 to state 2 with pressure p2, volume v2 and temperature Ta as shown in Fig. 3.6.1. For process 1-2, temperature remains constant is calculated as follows (i.e. T= T2 The gas equation for unit mass is given by Applying Boyle's law to process 1-2 pv RT PiV P2 V2 Multiplying above equation by molecular weight of gas M, PV 'V2 .(3.6.1) px (Mv) = MRT P2 pX = R,T=8.3143 T Where v is molal volume of gas. It is the volume occupied by I kg mole of any gas. R, is the universal gas constant. The value of v, and R, is same for all gases. .(3.8.1) Now let the gas at state 2 is further expanded to state 3. At state 3, pressure, volume and temperature are P3. V3 and T3 respectively. Applying Charle's law to process 2-3 Equation (3.8.1) is called Clapeyron-Mendeleev equation of state. Substituting the volume of p and T at NTP is p 101.325 kPa and T = 273 K (0° C), we get TT T T ..(3.6.2) 2 8.3143x 273 101.325 Km Substituting value of va2 from Equation (3.6.1) into Equation kg mol RX kN (3.6.2), we get 22.4 m kg mol Hence 1 kg mole of all gases occupy 22.4 m at NTP. 3.6 COMBINED GAS LAW OR P T PaVa = constant (. P2= P3) T3 CHARACTERISTIC EQUATION GAS .3.6.3) The magnitude of this constant depends upon particular gas under consideration and is denoted by R, where R is called --- *********; UQ. Derive Expression pv/T = constant with the help of Boyle's law and Charle's law. GTU Summer 2013) Define Gas constant. Derive characteristics equation of a perfect gas with the help of Boyle's law and Charle's law. characteristic gas constant. UQ. (GTU Summer 2018): For m kg of gas, UQ. T constant = mR GTU-Winter 2008, Summer 2018) or pv= mRT ..(3.6.4) - -- --- -- where P pressure of gas in Pa Definition : In actual practice, all the three variables i.e. pressure, volume and temperature change simultaneously. Therefore, Boyle's and Charle's law are combined to obtain relationship between pressure, volume and temperature. The equation so obtained is known as characteristic gas equation or combined gas law. Volume of gas in m m = mass of gas in kg R = Characteristie gas constant in J/kg K T Tenmperature of gas in K Equation (3.6.4) is called general gas equation, equation of state or characteristics gas equation. t 1( P,,T -PV = Constant 3.7 UNIT OF GAS CONSTANT Differentiate between gas constant and Universal gas constant. UQ. 2 P2V22) 3( P VT) (GTU-Winter 2019) -- ---- -- --- The characteristic gas constant is given by IN x m Volume m 3 Fig. 3.6.1: Combination of Boyle's and Charle's law R R =P T kgxK kgK =/kg K (New Syllabus w.e.f academic year 18-19) (G12-06) Tech-Neo Publications...A SACHIN SHAH Venture