CHEMICAL ENGINEERING

18 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

ideal gas is given by equation 2.25:

CvdTDPdvDdU.

PDRT/Mvand hence: dT/TD R/MCv dv/v

By definition: DCp/CvandCpDCvCR/M(from equation 2.27)

∴ R/MCvD1anddT/TD
 1
dv/v

Integrating between conditions 1 and 2 gives:

ln

T 2 /T 1 D

 1 ln v 2 /v 1 or

T 2 /T 1 D v 2 /v 1 ^1

P 1 v 1 /T 1 DP 2 v 2 /T 2 and hencev 1 /v 2 D

P 2 /P 1 

T 1 /T 2

and:
T 2 /T 1 D
P 2 /P 1
^1 /

Using the symbols given, the final temperature,T 2 DT
P/P 0
^1 /