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Contents
1
Table of isentropic relations for an ideal gas
2
1a===================
3
1aa===================
4
1===================
5
2===================
5.1
Table of isentropic relations for an ideal gas
Table of isentropic relations for an ideal gas
edit
[
T
2
T
1
]
{\displaystyle {\Bigg \lbrack }{\frac {T_{2}}{T_{1}}}{\Bigg \rbrack }}
=
{\displaystyle =\,\!}
(
p
2
p
1
)
γ
−
1
γ
{\displaystyle \left({\frac {p_{2}}{p_{1}}}\right)^{\frac {\gamma -1}{\gamma }}}
=
{\displaystyle =\,\!}
(
V
1
V
2
)
(
γ
−
1
)
{\displaystyle \left({\frac {V_{1}}{V_{2}}}\right)^{(\gamma -1)}}
=
{\displaystyle =\,\!}
(
ρ
2
ρ
1
)
(
γ
−
1
)
{\displaystyle \left({\frac {\rho _{2}}{\rho _{1}}}\right)^{(\gamma -1)}}
(
T
2
T
1
)
γ
γ
−
1
{\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)^{\frac {\gamma }{\gamma -1}}}
=
{\displaystyle =\,\!}
[
p
2
p
1
]
{\displaystyle {\Bigg \lbrack }{\frac {p_{2}}{p_{1}}}{\Bigg \rbrack }}
=
{\displaystyle =\,\!}
(
V
1
V
2
)
γ
{\displaystyle \left({\frac {V_{1}}{V_{2}}}\right)^{\gamma }}
=
{\displaystyle =\,\!}
(
ρ
2
ρ
1
)
γ
{\displaystyle \left({\frac {\rho _{2}}{\rho _{1}}}\right)^{\gamma }}
(
T
1
T
2
)
1
γ
−
1
{\displaystyle \left({\frac {T_{1}}{T_{2}}}\right)^{\frac {1}{\gamma -1}}}
=
{\displaystyle =\,\!}
(
p
1
p
2
)
1
γ
{\displaystyle \left({\frac {p_{1}}{p_{2}}}\right)^{\frac {1}{\gamma }}}
=
{\displaystyle =\,\!}
[
V
2
V
1
]
{\displaystyle {\Bigg \lbrack }{\frac {V_{2}}{V_{1}}}{\Bigg \rbrack }}
=
{\displaystyle =\,\!}
ρ
1
ρ
2
{\displaystyle {\frac {\rho _{1}}{\rho _{2}}}}
(
T
2
T
1
)
1
γ
−
1
{\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)^{\frac {1}{\gamma -1}}}
=
{\displaystyle =\,\!}
(
p
2
p
1
)
1
γ
{\displaystyle \left({\frac {p_{2}}{p_{1}}}\right)^{\frac {1}{\gamma }}}
=
{\displaystyle =\,\!}
V
1
V
2
{\displaystyle {\frac {V_{1}}{V_{2}}}}
=
{\displaystyle =\,\!}
[
ρ
2
ρ
1
]
{\displaystyle {\Bigg \lbrack }{\frac {\rho _{2}}{\rho _{1}}}{\Bigg \rbrack }}
1a===================
edit
T
2
T
1
{\displaystyle {\frac {T_{2}}{T_{1}}}}
=
{\displaystyle =\,\!}
T
2
T
1
{\displaystyle {\frac {T_{2}}{T_{1}}}}
=
{\displaystyle =\,\!}
(
p
2
p
1
)
γ
−
1
γ
{\displaystyle \left({\frac {p_{2}}{p_{1}}}\right)^{\frac {\gamma -1}{\gamma }}}
=
{\displaystyle =\,\!}
(
V
1
V
2
)
(
γ
−
1
)
{\displaystyle \left({\frac {V_{1}}{V_{2}}}\right)^{(\gamma -1)}}
=
{\displaystyle =\,\!}
(
ρ
2
ρ
1
)
(
γ
−
1
)
{\displaystyle \left({\frac {\rho _{2}}{\rho _{1}}}\right)^{(\gamma -1)}}
p
2
p
1
{\displaystyle {\frac {p_{2}}{p_{1}}}}
=
{\displaystyle =\,\!}
(
T
2
T
1
)
γ
γ
−
1
{\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)^{\frac {\gamma }{\gamma -1}}}
=
{\displaystyle =\,\!}
p
2
p
1
{\displaystyle {\frac {p_{2}}{p_{1}}}}
=
{\displaystyle =\,\!}
(
V
1
V
2
)
γ
{\displaystyle \left({\frac {V_{1}}{V_{2}}}\right)^{\gamma }}
=
{\displaystyle =\,\!}
(
ρ
2
ρ
1
)
γ
{\displaystyle \left({\frac {\rho _{2}}{\rho _{1}}}\right)^{\gamma }}
V
2
V
1
{\displaystyle {\frac {V_{2}}{V_{1}}}}
=
{\displaystyle =\,\!}
(
T
1
T
2
)
1
γ
−
1
{\displaystyle \left({\frac {T_{1}}{T_{2}}}\right)^{\frac {1}{\gamma -1}}}
=
{\displaystyle =\,\!}
(
p
1
p
2
)
1
γ
{\displaystyle \left({\frac {p_{1}}{p_{2}}}\right)^{\frac {1}{\gamma }}}
=
{\displaystyle =\,\!}
V
2
V
1
{\displaystyle {\frac {V_{2}}{V_{1}}}}
=
{\displaystyle =\,\!}
ρ
1
ρ
2
{\displaystyle {\frac {\rho _{1}}{\rho _{2}}}}
ρ
2
ρ
1
{\displaystyle {\frac {\rho _{2}}{\rho _{1}}}}
=
{\displaystyle =\,\!}
(
T
2
T
1
)
1
γ
−
1
{\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)^{\frac {1}{\gamma -1}}}
=
{\displaystyle =\,\!}
(
p
2
p
1
)
1
γ
{\displaystyle \left({\frac {p_{2}}{p_{1}}}\right)^{\frac {1}{\gamma }}}
=
{\displaystyle =\,\!}
V
1
V
2
{\displaystyle {\frac {V_{1}}{V_{2}}}}
=
{\displaystyle =\,\!}
ρ
2
ρ
1
{\displaystyle {\frac {\rho _{2}}{\rho _{1}}}}
1aa===================
edit
T
2
T
1
{\displaystyle {\frac {T_{2}}{T_{1}}}}
:
{\displaystyle :\,\!}
T
2
T
1
{\displaystyle {\frac {T_{2}}{T_{1}}}}
=
{\displaystyle =\,\!}
(
p
2
p
1
)
γ
−
1
γ
{\displaystyle \left({\frac {p_{2}}{p_{1}}}\right)^{\frac {\gamma -1}{\gamma }}}
=
{\displaystyle =\,\!}
(
V
1
V
2
)
(
γ
−
1
)
{\displaystyle \left({\frac {V_{1}}{V_{2}}}\right)^{(\gamma -1)}}
=
{\displaystyle =\,\!}
(
ρ
2
ρ
1
)
(
γ
−
1
)
{\displaystyle \left({\frac {\rho _{2}}{\rho _{1}}}\right)^{(\gamma -1)}}
p
2
p
1
{\displaystyle {\frac {p_{2}}{p_{1}}}}
:
{\displaystyle :\,\!}
(
T
2
T
1
)
γ
γ
−
1
{\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)^{\frac {\gamma }{\gamma -1}}}
=
{\displaystyle =\,\!}
p
2
p
1
{\displaystyle {\frac {p_{2}}{p_{1}}}}
=
{\displaystyle =\,\!}
(
V
1
V
2
)
γ
{\displaystyle \left({\frac {V_{1}}{V_{2}}}\right)^{\gamma }}
=
{\displaystyle =\,\!}
(
ρ
2
ρ
1
)
γ
{\displaystyle \left({\frac {\rho _{2}}{\rho _{1}}}\right)^{\gamma }}
V
2
V
1
{\displaystyle {\frac {V_{2}}{V_{1}}}}
:
{\displaystyle :\,\!}
(
T
1
T
2
)
1
γ
−
1
{\displaystyle \left({\frac {T_{1}}{T_{2}}}\right)^{\frac {1}{\gamma -1}}}
=
{\displaystyle =\,\!}
(
p
1
p
2
)
1
γ
{\displaystyle \left({\frac {p_{1}}{p_{2}}}\right)^{\frac {1}{\gamma }}}
=
{\displaystyle =\,\!}
V
2
V
1
{\displaystyle {\frac {V_{2}}{V_{1}}}}
=
{\displaystyle =\,\!}
ρ
1
ρ
2
{\displaystyle {\frac {\rho _{1}}{\rho _{2}}}}
ρ
2
ρ
1
{\displaystyle {\frac {\rho _{2}}{\rho _{1}}}}
:
{\displaystyle :\,\!}
(
T
2
T
1
)
1
γ
−
1
{\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)^{\frac {1}{\gamma -1}}}
=
{\displaystyle =\,\!}
(
p
2
p
1
)
1
γ
{\displaystyle \left({\frac {p_{2}}{p_{1}}}\right)^{\frac {1}{\gamma }}}
=
{\displaystyle =\,\!}
V
1
V
2
{\displaystyle {\frac {V_{1}}{V_{2}}}}
=
{\displaystyle =\,\!}
ρ
2
ρ
1
{\displaystyle {\frac {\rho _{2}}{\rho _{1}}}}
1===================
edit
T
2
T
1
{\displaystyle {\frac {T_{2}}{T_{1}}}}
=
{\displaystyle =\,\!}
⋅
{\displaystyle \cdot \,\!}
=
{\displaystyle =\,\!}
(
p
2
p
1
)
γ
−
1
γ
{\displaystyle \left({\frac {p_{2}}{p_{1}}}\right)^{\frac {\gamma -1}{\gamma }}}
=
{\displaystyle =\,\!}
(
V
1
V
2
)
(
γ
−
1
)
{\displaystyle \left({\frac {V_{1}}{V_{2}}}\right)^{(\gamma -1)}}
=
{\displaystyle =\,\!}
(
ρ
2
ρ
1
)
(
γ
−
1
)
{\displaystyle \left({\frac {\rho _{2}}{\rho _{1}}}\right)^{(\gamma -1)}}
p
2
p
1
{\displaystyle {\frac {p_{2}}{p_{1}}}}
=
{\displaystyle =\,\!}
(
T
2
T
1
)
γ
γ
−
1
{\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)^{\frac {\gamma }{\gamma -1}}}
=
{\displaystyle =\,\!}
⋅
{\displaystyle \cdot \,\!}
=
{\displaystyle =\,\!}
(
V
1
V
2
)
γ
{\displaystyle \left({\frac {V_{1}}{V_{2}}}\right)^{\gamma }}
=
{\displaystyle =\,\!}
(
ρ
2
ρ
1
)
γ
{\displaystyle \left({\frac {\rho _{2}}{\rho _{1}}}\right)^{\gamma }}
V
2
V
1
{\displaystyle {\frac {V_{2}}{V_{1}}}}
=
{\displaystyle =\,\!}
(
T
1
T
2
)
1
γ
−
1
{\displaystyle \left({\frac {T_{1}}{T_{2}}}\right)^{\frac {1}{\gamma -1}}}
=
{\displaystyle =\,\!}
(
p
1
p
2
)
1
γ
{\displaystyle \left({\frac {p_{1}}{p_{2}}}\right)^{\frac {1}{\gamma }}}
=
{\displaystyle =\,\!}
⋅
{\displaystyle \cdot \,\!}
=
{\displaystyle =\,\!}
ρ
1
ρ
2
{\displaystyle {\frac {\rho _{1}}{\rho _{2}}}}
ρ
2
ρ
1
{\displaystyle {\frac {\rho _{2}}{\rho _{1}}}}
=
{\displaystyle =\,\!}
(
T
2
T
1
)
1
γ
−
1
{\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)^{\frac {1}{\gamma -1}}}
=
{\displaystyle =\,\!}
(
p
2
p
1
)
1
γ
{\displaystyle \left({\frac {p_{2}}{p_{1}}}\right)^{\frac {1}{\gamma }}}
=
{\displaystyle =\,\!}
V
1
V
2
{\displaystyle {\frac {V_{1}}{V_{2}}}}
=
{\displaystyle =\,\!}
⋅
{\displaystyle \cdot \,\!}
2===================
edit
Table of isentropic relations for an ideal gas
edit
p
2
p
1
{\displaystyle {\frac {p_{2}}{p_{1}}}}
=
{\displaystyle =\,\!}
(
T
2
T
1
)
γ
γ
−
1
{\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)^{\frac {\gamma }{\gamma -1}}}
=
{\displaystyle =\,\!}
(
ρ
2
ρ
1
)
γ
{\displaystyle \left({\frac {\rho _{2}}{\rho _{1}}}\right)^{\gamma }}
=
{\displaystyle =\,\!}
(
V
1
V
2
)
γ
{\displaystyle \left({\frac {V_{1}}{V_{2}}}\right)^{\gamma }}
T
2
T
1
{\displaystyle {\frac {T_{2}}{T_{1}}}}
=
{\displaystyle =\,\!}
(
p
2
p
1
)
γ
−
1
γ
{\displaystyle \left({\frac {p_{2}}{p_{1}}}\right)^{\frac {\gamma -1}{\gamma }}}
=
{\displaystyle =\,\!}
(
ρ
2
ρ
1
)
(
γ
−
1
)
{\displaystyle \left({\frac {\rho _{2}}{\rho _{1}}}\right)^{(\gamma -1)}}
=
{\displaystyle =\,\!}
(
V
1
V
2
)
(
γ
−
1
)
{\displaystyle \left({\frac {V_{1}}{V_{2}}}\right)^{(\gamma -1)}}
ρ
2
ρ
1
{\displaystyle {\frac {\rho _{2}}{\rho _{1}}}}
=
{\displaystyle =\,\!}
(
T
2
T
1
)
1
γ
−
1
{\displaystyle \left({\frac {T_{2}}{T_{1}}}\right)^{\frac {1}{\gamma -1}}}
=
{\displaystyle =\,\!}
(
p
2
p
1
)
1
γ
{\displaystyle \left({\frac {p_{2}}{p_{1}}}\right)^{\frac {1}{\gamma }}}
=
{\displaystyle =\,\!}
V
1
V
2
{\displaystyle {\frac {V_{1}}{V_{2}}}}
V
2
V
1
{\displaystyle {\frac {V_{2}}{V_{1}}}}
=
{\displaystyle =\,\!}
(
T
1
T
2
)
1
γ
−
1
{\displaystyle \left({\frac {T_{1}}{T_{2}}}\right)^{\frac {1}{\gamma -1}}}
=
{\displaystyle =\,\!}
ρ
1
ρ
2
{\displaystyle {\frac {\rho _{1}}{\rho _{2}}}}
=
{\displaystyle =\,\!}
(
p
1
p
2
)
1
γ
{\displaystyle \left({\frac {p_{1}}{p_{2}}}\right)^{\frac {1}{\gamma }}}
