TITLE.PM5

264 ENGINEERING THERMODYNAMICS

dharm

/M-therm/th5-3.pm5

In other words, heat absorbed approximately equals the product of change of entropy and
mean absolute temperature.

Table 5.1. Summary of Formulae

S. No. Process Change of entropy (per kg)

1. General case (i)cv loge T
   T

2

1

+ R loge v

v

2

1

(in terms of T and v)

(ii)cv loge p

p

2

1

+ cv loge v

v

2

1

(in terms of p and v)

(iii) cp loge T

T

2

1

• R loge p
  p

2

1

(in terms of T and p)

2. Constant volume cv loge T
   T

2

1

3. Constant pressure cp loge T
   T

2

1

4. Isothermal R loge v
   v

2

1

5. Adiabatic Zero


6. Polytropic cv n
   n

−

−

F

HG

I

KJ

γ

1

loge T

T

2

1

5.18. Entropy Changes for an Open System

In an open system, as compared with closed system, there is additional change of entropy

due to the mass crossing the boundaries of the system. The net change of entropy of a system due

to mass transport is equal to the difference between the product of the mass and its specific

entropy at the inlet and at the outlet of the system. Therefore, the total change of entropy of the

system during a small interval is given by

dS ≥

dQ

T 0 + Σsi. dmi−Σs 0. dm^0

where, T 0 = Temperature of the surroundings,

si = Specific entropy at the inlet,

s 0 = Specific entropy at the outlet,

dmi= Mass entering the system, and

dm 0 = Mass leaving the system.

(Subscripts i and 0 refer to inlet and outlet conditions)

The above equation in general form can be written as

dS ≥
dQ
T 0

• ∑sdm. ...(5.37)
  In equation (5.37) entropy flow into the system is considered positive and entropy out-flow
  is considered negative. The equality sign is applicable to reversible process in which the heat
  interactions and mass transport to and from the system is accomplished reversibly. The inequality
  sign is applicable to irreversible processes.