Methane gas at 300.85°C at 3bar undergoes a reversible adiabatic expansion to 1bar, Assuming methane to be an ideal gas at these conditions what will be it's final temperature?
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Answer:
an adiabatic process, heat is not exchanged between the system and surroundings. In other words,
q
=
0
.
When a gas expands (or compresses) adiabatically, the relationship between its initial and final pressures
p
, volumes
V
, and temperatures
T
are given by the following:
p
1
V
γ
1
=
p
2
V
γ
2
T
1
V
γ
−
1
1
=
T
2
V
γ
−
1
2
T
1
p
(
1
−
γ
)
/
γ
1
=
T
2
p
(
1
−
γ
)
/
γ
2
Memorizing all these formulae is convenient, but not exactly necessary. The ideal gas law can be used together with any one of the formulae above to derive the other two.
The constant
γ
is the ratio between the constant pressure heat capacity and constant volume heat capacity.
γ
=
C
p
C
V
For a monoatomic species,
γ
=
5
/
3
. For a diatomic species,
γ
=
7
/
5
. For a polyatomic species,
γ
=
4
/
3
.
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