Lecture 15

• today:

• next lecture:

Chapter 1: Work, Heat and 1st Law of Thermodynamics

work, heat as energy transfers between system and environment

how state of system changes in response to work, heat

Ca lor imet r y ( spec i fic hea t and hea t o f transformation)

(1st law of Thermodynamics: energy conservation)

adiabatic process

Work-Energy Theorem

• earlier: how K and U is transformed into each other

• now: energy is transferred between system and environment (work and heat)

• associated with T: isothermal process (except phase changes)

Thermal energy

!K = Wc + Wdiss + Wextconservative forces:

dissipative:

external

!U = !Wc !Eth = !Wdiss

E m ec h = K + U (mot ion of system as a whole: macroscopic)vs. Eth (microscopic energy of atoms and bonds)

!Esys = !Eth + !Emech = Wext

isolated system: We x t = 0 ! !Es y s = 0 (energy conservation)

Eth = Kmicro + Umicro

Eint = Eth + Echem + Enucl Esys + Emech + Eint: here, Eint = Eth

moving atoms spring-like bonds

!T = 0

Work• energy transferred due to net force over a

distance (mechanical interaction): sign tells us which way transfer

• not a state variable

• energy transferred in thermal interaction e.g. water on stove

Energy transfer

Heat

W e x t = 0; ! E m ec h = 0, bu t ! E t h = 0

1st Law of Thermodynamics

• basic energy model (work included, but not heat) vice versa in thermodynamic... ener

• 1st law does not tell us , only

• change in other state variables (use other laws such as ideal-gas)

W + Q = !Es y s = !Em ec h + !Et h : here, !Em ec h = 0

E t h

! E th

! E th

Work in Ideal-gas Processes (I)

W = s f

s iF s ds (force parallel

to or opposi te to displacement )

F e x t = F g a s = ! p A(piston in equilibrium)

dW = F e x t dx = ! p A dx = ! pdV< ( > )0 (expansion / compression)

quasi-st at ic process:W = !

V f

V ipdV

(cannot t ake p ou t of in general)

= negative of area under pVcurve between V i and V f

Work in Ideal-gas Processes (II)• isochoric (constant V)

• isobaric (constant p)

• isothermal (constant T)

multi-step process(1 2 3):calculate W for each step and add not equal to W in 1 step (1 3)

Work done depends on path and not just initial and final states: forces not conservative; path is of thermodynamic states, not particle

W = ! V f

V ipdV = !

V f

V i

n R TV dV = ! n R T ln V f

V i

= ! p i V i ln V fV i

= ! p f V f ln V fV i

Heat

• more elusive than work: “something” flows from hot to cold object (heat fluid or caloric)

• Joule...heat is energy transferred: raise temperature by heating or doing work (different ways of transferring energy to/from system)

• thermal interaction (temperature difference): faster moleclues collider with slower (no macro.motion)

• heat is not state variable: energy transferred; units joule or calorie: 1 cal = heat to change 1 g water by 1 C 1 food calorie = 1 Cal = 1000 cal

Thermal energy vs. heat vs. temperature• Thermal energy (state variable): energy due to motion of atoms

(even for isolated system)

• Heat: energy transferred between system and environment; heat is not a form of energy or state variable; heat can cause thermal energy to change

• Temperature: state variable, related to thermal energy per molecule; temperature difference required for thermal interaction (observed temperature difference can be due to work done on system or heating

• fix volume by locking pin

• change pressure (unlock piston)

• heat transferred thru’ bottom (piston/sides insulated)

A Model...

pg a s = pa t m + M gA