Short Version : 18. Heat, Work, & First Law of Thermodynamics

18.1. The 1 st Law of Thermodynamics Either heating or stirring can raise T of the water. Joule’s apparatus 1 st Law of Thermodynamics: Increase in internal energy = Heat added  Work done Thermodynamic state variable = variable independent of history. e.g., U, T, P, V, … Not Q, W, … PE of falling weight  KE of paddle  Heat in water

18.2. Thermodynamic Processes Quasi-static process: Arbitrarily slow process such that system always stays arbitrarily close to thermodynamic equilibrium. Reversible process: Any changes induced by the process in the universe (system + environment) can be removed by retracing its path. Reversible processes must be quasi-static. Irreversible process: Part or whole of process is not reversible. e.g., any processes involving friction, free expansion of gas …. T water = T gas & rises slowly system always in thermodynamic equilibrium

Work & Volume Changes 面積 Work done by gas on piston

Isothermal Processes Isothermal process: T = constant.  Isothermal processes on ideal gas

Constant-Volume Processes & Specific Heat Constant-volume process ( isometric, isochoric, isovolumic ) : V = constant  C V = molar specific heat at constant volume Ideal gas: U = U(T)  for all processes isometric processes only for isometric processes  Non-ideal gas:

Isobaric Processes & Specific Heat Isobaric Process : constant P isobaric processes C P = molar specific heat at constant pressure Ideal gas, isobaric :  Ideal gas Isotherms

Adiabatic Processes Adiabatic process: Q = constant e.g., insulated system, quick changes like combustion, … Tactics  adiabat, ideal gas Prob. 66 Prob. 62 Adiabatic: larger  p cdf

TACTIC Adiabatic Equation Ideal gas, any process:  Adiabatic process:  

Example Diesel Power Fuel ignites in a diesel engine from the heat of compression (no spark plug needed). Compression is fast enough to be adiabatic. If the ignit temperature is 500  C, what compression ratio V max / V min is needed? Air’s specific heat ratio is  = 1.4, & before the compression the air is at 20  C.

Ideal Gas Processes

Cyclic Processes Cyclic Process : system returns to same thermodynamic state periodically.

Example Finding the Work An ideal gas with  = 1.4 occupies 4.0 L at 300 K & 100 kPa pressure. It’s compressed adiabatically to ¼ of original volume, then cooled at constant V back to 300 K, & finally allowed to expand isothermally to its original V. How much work is done on the gas? AB (adiabatic): BC (isometric): CA (isothermal): work done by gas:

18.3. Specific Heats of an Ideal Gas  Ideal gas: Experimental values ( room T ): For monatomic gases,   5/3, e.g., He, Ne, Ar, …. For diatomic gases,   7/5 = 1.4, C V = 5R/2, e.g., H 2, O 2, N 2, …. For tri-atomic gases,   1.3, C V = 3.4R, e.g., SO 2, NO 2, ….  Degrees of freedom (DoF) = number of independent coordinates required to describe the system Single atom: DoF = 3 (transl) For low T ( vib modes not active ) : Rigid diatomic molecule : DoF = 5 (3 transl + 2 rot) Rigid triatomic molecule : DoF = 6 (3 transl + 3 rot)

The Equipartition Theorem Equipartition theorem ( kinetic energy version): For a system in thermodynamic equilibrium, each degree of freedom of a rigid molecule contributes ½ kT to its average energy. Equipartition theorem ( general version): For a system in thermodynamic equilibrium, each degree of freedom described by a quadratic term in the energy contributes ½ kT to its average energy. DoF ( f )CVCV CPCP  Monatomic33/25/25/3 Diatomic55/27/27/5 Triatomic6344/3

Example Gas Mixture A gas mixture consists of 2.0 mol of oxygen (O 2 ) & 1.0 mol of Argon (Ar). Find the volume specific heat of the mixture.

Quantum Effects C V of H 2 gas as function of T. Below 20 K hydrogen is liquid, above 3200 K it dissociates into individual atoms. Quantum effect: Each mechanism has a threshold energy. E transl < E rot < E vib Translation rotation+Translation rotation+Translation+vibration

Reprise Quasi-static process : Arbitrarily slow process such that system always stays arbitrarily close to thermodynamic equilibrium. Reversible process: Any changes induced by the process in the universe (system + environment) can be removed by retracing its path. a  c : Free expansion with no dissipative work. c  b : Adiabatic. a  d : Adiabatic. d  b : Free expansion with no dissipative work. a  e : Adiabatic. e  b : Adiabatic dissipative work. Insulated gas 1 st law: The net adiabatic work done in all 3 processes are equal (shaded areas are equal). Dissipative work: Work done on system without changing its configuration, irreversible.