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Reversible and Irreversible Expansion and Compression Processes

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Use this Demonstration to identify isothermal, reversible-adiabatic and irreversible-adiabatic processes of an ideal gas in a step-by-step procedure. After starting and with "new problem" selected, the Demonstration shows either an expansion or a compression process, and either a pressure-temperature or pressure-volume diagram. Select your answer from the possible options (a, b, c, d, e) and then select "show solution" to see the correct answer. The "hint" button provides a hint for each step, and once "show solution" is selected, you cannot go back.

Details

The first law of thermodynamics, representing the conservation of energy, is:
ΔU=Q-W
,
where
ΔU
is the change to internal energy of the system,
Q
is heat added to the system and
W
is the work done by the system. In adiabatic processes,
Q=0
, while
Q≠0
in isothermal processes with external pressure
P
ext
≠0
. Expansion-compression work
W
for all four processes is calculated from:
W=-∫
P
ext
dV
,
where
P
ext
is the external pressure and
W
is in units of kJ/mol. The external pressure and the gas pressure are equal for a reversible process, whereas for an irreversible process the external pressure is equal to the final pressure. Change in internal energy is calculated from:
ΔU=
C
V
(
T
2
-
T
1
)
.
Initial state:
V
1
=
R
T
1
P
1
,
where the subscript
1
refers to the initial state,
R
is the ideal gas constant (kJ/mol K),
V
is volume (
3
m
/mol
),
T
is temperature (K) and
P
is pressure (Pa).
For an isothermal process:
V
2
=
R
T
1
P
2
,
where the subscript
2
refers to the final condition.
Reversible work:
W=-R
T
1
ln
V
2
V
1
.
Irreversible work:
W=-
P
2
(
V
2
-
V
1
)
.
For an adiabatic process on an ideal diatomic gas:
γ=
7
5
,
C
V
=
5R
2
,
W=
C
V
(
T
2
-
T
1
)
,
where
γ=
C
p
C
V
,
C
V
is the constant volume heat capacity and
C
p
is the constant pressure heat capacity (kJ/(mol K)).
Reversible process:
V
2
=
V
1
1
γ
P
1
P
2
,
T
2
=
T
1
γ-1
V
1
V
2
.
Irreversible process:
T
2
=
T
1
-
P
2
(
V
2
-
V
1
)
C
V
,
V
2
=
R(
C
V
T
1
+
P
2
V
1
)
P
2
(
C
V
R)
.

References

[1] J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics, 2nd ed., Upper Saddle River, NJ: Prentice Hall, 2012.

External Links

Permanent Citation

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