Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodynamics 45

(b) For A -+ B, the increase of the internal energy is

AU = &',,AT = C,,PA(VB - VA)/R = 3W/2 = 1.5 x lo5 J.

2x'05[ 1 lo5 *:-A I

C

I I I

I I

II I I

0 1.0 1.5 2.0

v(m3)

Fig. 1.17.

(c) By the first law of thermodynamics, the heat absorbed during A +
B is W + AU = 2.5 x lo5 3.

(d) For B + C, the adiabatic process of an monatomic ideal gas sat-
isfies the equation

pV7 = const. , where 7 = C,/C, = 5/3.

Thus p~v; = pcv,' and pc = (vB/vc)7pB = 1.24 x lo5 N/rn2.
In the process of reversible adiabatic expansion, the change in entropy is
AS = 0. This is shown by the calculation in detail as follows:

TC VC

TB VB

TcV2-l

= nC, In =o.

~Bv2-l

AS = nC,, In - + nR In -

1050

A mole of an ideal gas undergoes a reversible isothermal expansion