TITLE.PM5

118 ENGINEERING THERMODYNAMICS

dharm

M-therm/th4-1.pm5

Fig. 4.10. Free expansion.
∴ For a free expansion of a perfect gas,
cvT 1 = cvT 2 i.e., T 1 = T 2
That is, for a perfect gas undergoing a free expansion, the initial temperature is equal to the
final temperature.
Table 4.1
Summary of Processes for Perfect Gas (Unit mass)

Process Index Heat added pdv

1

2

z p, v, T Specific heat, c

n relations

Constant

pressure n = 0 cp(T^2 – T^1 ) p(v^2 – v^1 )

T

T

v

v

2

1

=^2

1

cp

Constant

volume n = ∞ cv(T^2 – T^1 )0

T

T

p

p

1

2

=^1

2 cv

Constant

temperature n =1 pv

v

11 logev

2

1

pv 11 logevv^2

1 p^1 v^1 = p^2 v^2 ∞

pv 11 γγ=pv2 2

Reversible

adiabatic n = γ 0 pv^11 p v2 2

1

−

−γ

T

T

v

v

2

1

1

2

1

=F

HG

I

KJ

−γ

0

=

F

HG

I

KJ

−

p

P

2

1

γ 1

γ

Polytropic n = n cT Tn()^21 −

pv p v

n

11 2 2

1

−

−

pv 11 nn=p v2 2 cc n

n v n

= −

−

F

HG

I

KJ

γ

1

= F −−

HG

I

KJ

×−

c nn

TT

v

γ

1

() 21

T

T

v

v

n

2

1

1

2

1

=F

HG

I

KJ

−

= −− ×

−

γ

γ

n

1 work

done (non flow)

=F

HG

I

KJ

−

p

p

n

2 n

1

1

Note. Equations must be used keeping dimensional consistence.