1. 1. CHAPTER 3 Ideal gases and thermodynamic processes Missam Raza Mechanical Dept LJ Polytechnic
2. 2. Ideal Gas Laws Introduction Ideal Gas Equation Missam Raza Mechanical Dept LJ Polytechnic P V = n R T Universal Gas ConstantVolume No. of moles Temperature Pressure R = 0.0821 atm L / mol K R = 8.314 kPa L / mol K
3. 3. Ideal Gas Laws Introduction Missam Raza Mechanical Dept LJ Polytechnic PV = nRT P = pressure V = volume T = temperature (Kelvin) n = number of moles R = gas constant Standard Temperature and Pressure (STP) T = 0 oC or 273 K P = 1 atm = 101.3 kPa = 760 mm Hg Solve for constant (R) PV nT = R Substitute values: (1 atm) (22.4 L) (1 mole)(273 K) R = 0.0821 atm L / mol K or R = 8.31 kPa L / mol K R = 0.0821 atm L mol K Recall: 1 atm = 101.3 kPa (101.3 kPa) ( 1 atm) = 8.31 kPa L mol K 1 mol = 22.4 L @ STP
4. 4. Thermodynamic Processes Introduction States of a thermodynamic system can be changed by interacting with its surrounding through work and heat. When this change occurs in a system, it is said that the system is undergoing a process. A thermodynamic cycle is a sequence of different processes that begins and ends at the same thermodynamic state Missam Raza Mechanical Dept LJ Polytechnic
5. 5. Thermodynamic Processes Types Some sample processes: Isothermal process: temperature is constant T=C Isobaric process: pressure is constant, P=C Isentropic process: entropy is constant, s=C Constant-volume process, v=C Adiabatic process: no heat transfer, Q=0 Missam Raza Mechanical Dept LJ Polytechnic
6. 6. Thermodynamic Processes Process-1 Use ideal gas assumption (closed system): Missam Raza Mechanical Dept LJ Polytechnic 2 1 2 1 1 2 Isothermal process: T=constant Energy balance U=Q-W, for ideal gas U= H=0 since both are functions of temperature only Q=W, W= P ln ln Isobaric process: mRT dV dV dV mRT V V V P mRT mRT V P 2 2 1 1 2 1 2 1 2 1 2 2 1 1 2 1 P=constant U=Q-W, W= PdV=P dV=P(V ) ( ) ( ) ( ) ( ) ( ) V Q U P V V U U P V V U PV U PV H H H
7. 7. Thermodynamic Processes Process-2 Use ideal gas assumption (closed system): Missam Raza Mechanical Dept LJ Polytechnic v v Constant volume process: V=constant Q-W= U, W= 0, no work done Q= U=m u=m c Adiabatic process: Q=0 Q-W= U, -W= U - W=dU (infinitesimal increment of work and energy) dU+PdV=0, mc 0 v PdV dT mRT dT dV V c v 2 2 2 1 1 1 1 1 2 2 1 0, , integrate and assume c =constant ln ln , v v v R kc cRT dT dV dT dV V R T V c T V T V V R T V T V V
8. 8. Thermodynamic Processes Process-3 Use ideal gas assumption (closed system): Missam Raza Mechanical Dept LJ Polytechnic 2 1 1 2 1 1 2 2 2 1 2 1 2 2 1 2 1 1 2 2 2 1 1 1 1 ( 1) 1 1 1 , from ideal gas relation PV=RT, , substitute , multiply from both sides , k k k k k T V T V V T P V T P T T P T T T P T T P P V T P P and 2 1 1 2 2 k Also and tan For an ideal gas undergoing adiabatic process k k k V PV PV pV cons t
9. 9. Thermodynamic Processes Process-4 Polytropic Process: its P-V relation can be expressed as PVn = constant, where n is a constant for a specific process Isothermal, T=constant, if the gas is an ideal gas then PV=RT=constant, n=1 Isobaric, P=constant, n=0 (for all substances) Constant-volume, V=constant, V=constant(P)(1/n), n= (for all substances) Adiabatic process, n=k for an ideal gas Missam Raza Mechanical Dept LJ Polytechnic
10. 10. Thermodynamic Processes Process-4 Missam Raza Mechanical Dept LJ Polytechnic 1 1 2 2 2 2 1 1 1 1 2 1 11 1 2 2 1 1 1 1 2 1 1 ( ) ( ) ( ) ( ) 1 1 n n n n n n n n n n PV PV PV W PdV PV V dV PV PV PV PV V dV V V n n
11. 11. THANK YOU Missam Raza Mechanical Dept LJ Polytechnic