Adiabatic Expansion and Compression of an Ideal Gas

compression, top graph

initial temp

T

i

(K)

160

final temp

T

f

(K)

210

moles n

5.362

Γ

5

3

7

5

expansion, bottom graph

initial temp

T

i

(K)

210

final temp

T

f

(K)

160

moles n

5.362

Γ

5

3

7

5

work =

p

i

γ

v

i



1-γ

v

f

-

1-γ

v

i



1-γ

= -13.2002 J

compression of an ideal gas when q = 0

work =

p

i

γ

v

i



1-γ

v

f

-

1-γ

v

i



1-γ

= 13.2002 J

expansion of an ideal gas when q = 0

This Demonstration shows adiabatic compression/expansions of an ideal gas, a frequently invoked thermodynamic process (e.g., in a Carnot cycle). Each graphic displays three curves. The two blue curves represent the isotherms of the initial and final temperature; the red line is the adiabatic curve.

As you vary the initial and final temperatures

T

i

and

T

f

, you can see where the isotherms shift and where they cross the adiabatic curve. The area shaded in blue between these two points represents the work done on the gas. Thus, when the ideal gas "does" work "on" the surroundings, the value of work shown should be positive. To the right of each curve, there is an image of two pistons. As you vary from an initial to a final volume, you can see to where the gas has been expanded or compressed by the location of the piston head (labeled

v

f

) on the right side, compared to its initial position, denoted by

v

i

. Note that the result depends on the heat capacity ratio

γ=

C

p



C

v

. For a monotomic ideal gas,

γ=5/3

, for a diatomic ideal gas,

γ=7/5

.