Problems and Solutions on Thermodynamics and Statistical Mechanics

48 Problems €4 Solutions on Thermodynamics €4 Statistical Mechanics

+ AV

-AV

T

Fig. 1.19

I I I

1 AT 1 AU 1 AS

1. (+AV) (slow) (conduct)


2. (+AV) (slow) (insulate)


3. (+AV) (fast) (insulate)


4. (+AV) (fast) (conduct)
   5. (-AV) [fast) (conduct)

( wis co ns in)

Solution:

(1) For isothernial expansion, AT = 0, AU = 0, and

AS = R- AV > 0, Ap = -AV -P < 0.

V V

(2) For adiabatic expansion, AQ = 0. Because the process proceeds

very slowly it can be taken as a reversible process of quasistatic states, then

AS = 0. The adiabatic process satisfies pV7 = const. While V increases,

p decreases, i.e., Ap < 0; and the internal energy of the system decreases

because it does work externally, thus AU < 0, or AT < 0.

(3) The process is equivalent to adiabatic free expansion of an ideal

gas, thus AS > 0, AU = 0, AT = 0, Ap < 0.

(4) The result is as the same as that of isothermal free expansion, thus

AT = 0, AU = 0, AS > 0, Ap < 0.

(5) The result is the same as that of isothermal free compression, thus

The above are summarized in the table below

AT = 0, AU = 0, Ap > 0, AS < 0.