Chap 4. Macroscopic parameters and their measurement

Most of stuff in this chapter will be skipped!

4-1. Heat capacity and Specific heat

macroscopic system

[eqn: \{y_1 , y_2 , ... \}] : macroscopic parameters other than T like V or P, ... .

Add □Q and keep one or some of parameters y fixed.

If the resulting temperature change is dT,

We define "heat capacity" of the system

[eqn: C_y == left ( □Q over dT right) _y]

In general [eqn: C_y = C_y (T, y )~]

* "specific heat"

[eqn: C_y &== &1 over nu C_y] : molar specific heat (per mole)

[eqn: C' _y & == & 1 over m C_y] : specific heat per gram.

Using the 2nd law ([eqn: □Q = TdS] )

[eqn: C_y = left ( □Q over dT right ) _y = TdS over dT right | _y = T left ( ∂S over ∂T right ) _y]

If all external parameters are kept fixed,

there is no work([eqn: □ W = phi] ).

∀	[eqn: C_y = TdS over dT right | _y = dE over dT right | _y = left ( ∂E over ∂T right ) _y ~]

(eg.)	[eqn: C_V = left ( ∂E over ∂T right ) _V ~](V : fixed → no work by pressure)

* entropy

[eqn: S_b - S_a int from { a atop (eg.) } to b □Q over T ~]

Suppose all parameters y other than T are kept constant.

∀ [eqn: □ Q = C_y dT~]

[eqn: S_b - S_a = int from T_a to T_b {C_y dT} over T]

∴

4-2 Few miscellaneous

* temperature

T : absolute temperature (K : Kelvin)

[eqn: k_B] = [eqn: 1.38 times 10 ^-16 ergs/K]

[eqn: 1eV ~ =~k_B T ~~~∀~T approx 10^4 K]

* Extensive & intensive parameters

value of a parameter = y

value of the parameter = y1

"      "      = y2

If [eqn: y = y_1 + y_2], then y : extensive parameter.

If [eqn: y = y_1 = y_2], then y : intensive parameter.

(eg.)	· extensive : volume, heat capacity, total energy, entropy, ...

· intensive : density, temperature, pressure, energy density, specific heat, entropy density, ... .

(H. W.) 3, 4, 5.