A certain volume of dry gas is expanded to three times its volume adiabatically. Calculate the final pressure and temperature assuming ideal behavior of the gas (1.4=γ).
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Answer:
Explanation:
Let V
1
be the initial volume of dry air at NTP
(a) Isothermally expansion: During isothermal expansion, the temperature remains the same throughout. Hence, final temperature will be 273K.
Since, P
1
V
1
=P
2
V
2
P
2
=
V
2
P
1
V
1
=
4V
1
1×V
1
=0.25atm
(b) Adiabatic expansion:
T
2
T
1
=(
V
1
V
2
)
γ−1
T
2
273
=(
V
1
4V
1
)
1.4−1
=4
0.4
T
2
=
4
0.4
273
=156.79K
Final Pressure:
P
2
P
1
=(
V
1
V
2
)
γ
P
2
1
=(
V
1
4V
1
)
1.4
=4
1.4
P
2
=
4
1.4
1
=0.143atm
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