11/18/2019 1 11/18/2019 PHY 711 Fall 2019 -- Lecture 33 1 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 33: Chapter 11 in F & W: Heat conduction 1. Basic equations 2. Boundary value problems 11/18/2019 PHY 711 Fall 2019 -- Lecture 33 2 11/18/2019 PHY 711 Fall 2019 -- Lecture 33 3 Conduction of heat j h T(r,t) 3 0 0 0 Enthalpy of a system at constant pressure non uniform temperature , mass density and heat capacity , , p p V p T t c H c T t T dr H T p r r 1 2 3
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11/18/2019
1
11/18/2019 PHY 711 Fall 2019 -- Lecture 33 1
PHY 711 Classical Mechanics and Mathematical Methods
10-10:50 AM MWF Olin 103
Plan for Lecture 33:
Chapter 11 in F & W:
Heat conduction
1. Basic equations
2. Boundary value problems
11/18/2019 PHY 711 Fall 2019 -- Lecture 33 2
11/18/2019 PHY 711 Fall 2019 -- Lecture 33 3
Conduction of heat
jh
T(r,t)
30 0 0
Enthalpy of a system at constant pressure
non uniform temperature ,
mass density and heat capacity
,
,
p
p
V
p
T t
c
H c T t T d r H T p
r
r
1
2
3
11/18/2019
2
11/18/2019 PHY 711 Fall 2019 -- Lecture 33 4
Note that in this treatment we are considering a system at constant pressure p
Notation: Heat added to system --
External work done on system --
Internal energy --
dQ TdS
dW pdV
dE dQ dW T
Entropy --
Enthalpy -- ( )
dS pdV
dS
dH d E pV TdS Vdp
3
Heat capacity at constant pressure:
p
p pp
p
p
dQ H SC T
dT T
c
T
C d r
More generally, note that cp can depend on T; we are assuming that dependence to be trivial.