User:Ac44ck/Sandbox 1

Table of isentropic relations for an ideal gas

${\Bigg \lbrack }{\frac {T_{2}}{T_{1}}}{\Bigg \rbrack }$	$=\,\!$	$\left({\frac {p_{2}}{p_{1}}}\right)^{\frac {\gamma -1}{\gamma }}$	$=\,\!$	$\left({\frac {V_{1}}{V_{2}}}\right)^{(\gamma -1)}$	$=\,\!$	$\left({\frac {\rho _{2}}{\rho _{1}}}\right)^{(\gamma -1)}$
$\left({\frac {T_{2}}{T_{1}}}\right)^{\frac {\gamma }{\gamma -1}}$	$=\,\!$	${\Bigg \lbrack }{\frac {p_{2}}{p_{1}}}{\Bigg \rbrack }$	$=\,\!$	$\left({\frac {V_{1}}{V_{2}}}\right)^{\gamma }$	$=\,\!$	$\left({\frac {\rho _{2}}{\rho _{1}}}\right)^{\gamma }$
$\left({\frac {T_{1}}{T_{2}}}\right)^{\frac {1}{\gamma -1}}$	$=\,\!$	$\left({\frac {p_{1}}{p_{2}}}\right)^{\frac {1}{\gamma }}$	$=\,\!$	${\Bigg \lbrack }{\frac {V_{2}}{V_{1}}}{\Bigg \rbrack }$	$=\,\!$	${\frac {\rho _{1}}{\rho _{2}}}$
$\left({\frac {T_{2}}{T_{1}}}\right)^{\frac {1}{\gamma -1}}$	$=\,\!$	$\left({\frac {p_{2}}{p_{1}}}\right)^{\frac {1}{\gamma }}$	$=\,\!$	${\frac {V_{1}}{V_{2}}}$	$=\,\!$	${\Bigg \lbrack }{\frac {\rho _{2}}{\rho _{1}}}{\Bigg \rbrack }$

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${\frac {T_{2}}{T_{1}}}$	$=\,\!$	${\frac {T_{2}}{T_{1}}}$	$=\,\!$	$\left({\frac {p_{2}}{p_{1}}}\right)^{\frac {\gamma -1}{\gamma }}$	$=\,\!$	$\left({\frac {V_{1}}{V_{2}}}\right)^{(\gamma -1)}$	$=\,\!$	$\left({\frac {\rho _{2}}{\rho _{1}}}\right)^{(\gamma -1)}$
${\frac {p_{2}}{p_{1}}}$	$=\,\!$	$\left({\frac {T_{2}}{T_{1}}}\right)^{\frac {\gamma }{\gamma -1}}$	$=\,\!$	${\frac {p_{2}}{p_{1}}}$	$=\,\!$	$\left({\frac {V_{1}}{V_{2}}}\right)^{\gamma }$	$=\,\!$	$\left({\frac {\rho _{2}}{\rho _{1}}}\right)^{\gamma }$
${\frac {V_{2}}{V_{1}}}$	$=\,\!$	$\left({\frac {T_{1}}{T_{2}}}\right)^{\frac {1}{\gamma -1}}$	$=\,\!$	$\left({\frac {p_{1}}{p_{2}}}\right)^{\frac {1}{\gamma }}$	$=\,\!$	${\frac {V_{2}}{V_{1}}}$	$=\,\!$	${\frac {\rho _{1}}{\rho _{2}}}$
${\frac {\rho _{2}}{\rho _{1}}}$	$=\,\!$	$\left({\frac {T_{2}}{T_{1}}}\right)^{\frac {1}{\gamma -1}}$	$=\,\!$	$\left({\frac {p_{2}}{p_{1}}}\right)^{\frac {1}{\gamma }}$	$=\,\!$	${\frac {V_{1}}{V_{2}}}$	$=\,\!$	${\frac {\rho _{2}}{\rho _{1}}}$

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${\frac {T_{2}}{T_{1}}}$	$:\,\!$	${\frac {T_{2}}{T_{1}}}$	$=\,\!$	$\left({\frac {p_{2}}{p_{1}}}\right)^{\frac {\gamma -1}{\gamma }}$	$=\,\!$	$\left({\frac {V_{1}}{V_{2}}}\right)^{(\gamma -1)}$	$=\,\!$	$\left({\frac {\rho _{2}}{\rho _{1}}}\right)^{(\gamma -1)}$
${\frac {p_{2}}{p_{1}}}$	$:\,\!$	$\left({\frac {T_{2}}{T_{1}}}\right)^{\frac {\gamma }{\gamma -1}}$	$=\,\!$	${\frac {p_{2}}{p_{1}}}$	$=\,\!$	$\left({\frac {V_{1}}{V_{2}}}\right)^{\gamma }$	$=\,\!$	$\left({\frac {\rho _{2}}{\rho _{1}}}\right)^{\gamma }$
${\frac {V_{2}}{V_{1}}}$	$:\,\!$	$\left({\frac {T_{1}}{T_{2}}}\right)^{\frac {1}{\gamma -1}}$	$=\,\!$	$\left({\frac {p_{1}}{p_{2}}}\right)^{\frac {1}{\gamma }}$	$=\,\!$	${\frac {V_{2}}{V_{1}}}$	$=\,\!$	${\frac {\rho _{1}}{\rho _{2}}}$
${\frac {\rho _{2}}{\rho _{1}}}$	$:\,\!$	$\left({\frac {T_{2}}{T_{1}}}\right)^{\frac {1}{\gamma -1}}$	$=\,\!$	$\left({\frac {p_{2}}{p_{1}}}\right)^{\frac {1}{\gamma }}$	$=\,\!$	${\frac {V_{1}}{V_{2}}}$	$=\,\!$	${\frac {\rho _{2}}{\rho _{1}}}$

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${\frac {T_{2}}{T_{1}}}$	$=\,\!$	$\cdot \,\!$	$=\,\!$	$\left({\frac {p_{2}}{p_{1}}}\right)^{\frac {\gamma -1}{\gamma }}$	$=\,\!$	$\left({\frac {V_{1}}{V_{2}}}\right)^{(\gamma -1)}$	$=\,\!$	$\left({\frac {\rho _{2}}{\rho _{1}}}\right)^{(\gamma -1)}$
${\frac {p_{2}}{p_{1}}}$	$=\,\!$	$\left({\frac {T_{2}}{T_{1}}}\right)^{\frac {\gamma }{\gamma -1}}$	$=\,\!$	$\cdot \,\!$	$=\,\!$	$\left({\frac {V_{1}}{V_{2}}}\right)^{\gamma }$	$=\,\!$	$\left({\frac {\rho _{2}}{\rho _{1}}}\right)^{\gamma }$
${\frac {V_{2}}{V_{1}}}$	$=\,\!$	$\left({\frac {T_{1}}{T_{2}}}\right)^{\frac {1}{\gamma -1}}$	$=\,\!$	$\left({\frac {p_{1}}{p_{2}}}\right)^{\frac {1}{\gamma }}$	$=\,\!$	$\cdot \,\!$	$=\,\!$	${\frac {\rho _{1}}{\rho _{2}}}$
${\frac {\rho _{2}}{\rho _{1}}}$	$=\,\!$	$\left({\frac {T_{2}}{T_{1}}}\right)^{\frac {1}{\gamma -1}}$	$=\,\!$	$\left({\frac {p_{2}}{p_{1}}}\right)^{\frac {1}{\gamma }}$	$=\,\!$	${\frac {V_{1}}{V_{2}}}$	$=\,\!$	$\cdot \,\!$

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Table of isentropic relations for an ideal gas

${\frac {p_{2}}{p_{1}}}$	$=\,\!$	$\left({\frac {T_{2}}{T_{1}}}\right)^{\frac {\gamma }{\gamma -1}}$	$=\,\!$	$\left({\frac {\rho _{2}}{\rho _{1}}}\right)^{\gamma }$	$=\,\!$	$\left({\frac {V_{1}}{V_{2}}}\right)^{\gamma }$
${\frac {T_{2}}{T_{1}}}$	$=\,\!$	$\left({\frac {p_{2}}{p_{1}}}\right)^{\frac {\gamma -1}{\gamma }}$	$=\,\!$	$\left({\frac {\rho _{2}}{\rho _{1}}}\right)^{(\gamma -1)}$	$=\,\!$	$\left({\frac {V_{1}}{V_{2}}}\right)^{(\gamma -1)}$
${\frac {\rho _{2}}{\rho _{1}}}$	$=\,\!$	$\left({\frac {T_{2}}{T_{1}}}\right)^{\frac {1}{\gamma -1}}$	$=\,\!$	$\left({\frac {p_{2}}{p_{1}}}\right)^{\frac {1}{\gamma }}$	$=\,\!$	${\frac {V_{1}}{V_{2}}}$
${\frac {V_{2}}{V_{1}}}$	$=\,\!$	$\left({\frac {T_{1}}{T_{2}}}\right)^{\frac {1}{\gamma -1}}$	$=\,\!$	${\frac {\rho _{1}}{\rho _{2}}}$	$=\,\!$	$\left({\frac {p_{1}}{p_{2}}}\right)^{\frac {1}{\gamma }}$