User:Ac44ck/Sandbox 1

Table of isentropic relations for an ideal gas

 * {| style="bgcolor:white" cellpadding=5


 * align="center" | $$\Bigg\lbrack \frac{T_2}{T_1} \Bigg\rbrack$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_2}{p_1} \right )^\frac {\gamma-1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\left (\frac{V_1}{V_2} \right )^{(\gamma-1)}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{\rho_2}{\rho_1} \right )^{(\gamma - 1)}$$
 * align="center" | $$ \left (\frac{T_2}{T_1} \right )^\frac {\gamma}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\Bigg\lbrack \frac {p_2} {p_1} \Bigg\rbrack$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\left (\frac{V_1}{V_2} \right )^{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{\rho_2}{\rho_1} \right )^{\gamma}$$
 * align="center" | $$ \left (\frac{T_1}{T_2} \right )^\frac {1}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_1}{p_2} \right )^\frac {1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\Bigg\lbrack \frac{V_2}{V_1} \Bigg\rbrack$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{\rho_1}{\rho_2}$$
 * align="center" | $$ \left (\frac{T_2}{T_1} \right )^\frac {1}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_2}{p_1} \right )^\frac {1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{V_1}{V_2}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\Bigg\lbrack \frac{\rho_2}{\rho_1} \Bigg\rbrack$$
 * }
 * align="center" | $$\frac{V_1}{V_2}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\Bigg\lbrack \frac{\rho_2}{\rho_1} \Bigg\rbrack$$
 * }
 * }

=1a====================


 * {| style="bgcolor:white" cellpadding=5


 * align="center" | $$\frac{T_2}{T_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{T_2}{T_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_2}{p_1} \right )^\frac {\gamma-1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\left (\frac{V_1}{V_2} \right )^{(\gamma-1)}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{\rho_2}{\rho_1} \right )^{(\gamma - 1)}$$
 * align="center" | $$\frac {p_2} {p_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{T_2}{T_1} \right )^\frac {\gamma}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac {p_2} {p_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\left (\frac{V_1}{V_2} \right )^{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{\rho_2}{\rho_1} \right )^{\gamma}$$
 * align="center" | $$\frac{V_2}{V_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{T_1}{T_2} \right )^\frac {1}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_1}{p_2} \right )^\frac {1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{V_2}{V_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{\rho_1}{\rho_2}$$
 * align="center" | $$\frac{\rho_2}{\rho_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{T_2}{T_1} \right )^\frac {1}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_2}{p_1} \right )^\frac {1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{V_1}{V_2}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{\rho_2}{\rho_1}$$
 * }
 * align="center" | $$\frac{V_1}{V_2}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{\rho_2}{\rho_1}$$
 * }
 * }

=1aa====================


 * {| style="bgcolor:white" cellpadding=5


 * align="center" | $$\frac{T_2}{T_1}$$
 * align="center" | $$:\,\!$$
 * align="center" | $$\frac{T_2}{T_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_2}{p_1} \right )^\frac {\gamma-1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\left (\frac{V_1}{V_2} \right )^{(\gamma-1)}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{\rho_2}{\rho_1} \right )^{(\gamma - 1)}$$
 * align="center" | $$\frac {p_2} {p_1}$$
 * align="center" | $$:\,\!$$
 * align="center" | $$ \left (\frac{T_2}{T_1} \right )^\frac {\gamma}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac {p_2} {p_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\left (\frac{V_1}{V_2} \right )^{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{\rho_2}{\rho_1} \right )^{\gamma}$$
 * align="center" | $$\frac{V_2}{V_1}$$
 * align="center" | $$:\,\!$$
 * align="center" | $$ \left (\frac{T_1}{T_2} \right )^\frac {1}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_1}{p_2} \right )^\frac {1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{V_2}{V_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{\rho_1}{\rho_2}$$
 * align="center" | $$\frac{\rho_2}{\rho_1}$$
 * align="center" | $$:\,\!$$
 * align="center" | $$ \left (\frac{T_2}{T_1} \right )^\frac {1}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_2}{p_1} \right )^\frac {1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{V_1}{V_2}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{\rho_2}{\rho_1}$$
 * }
 * align="center" | $$\frac{V_1}{V_2}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{\rho_2}{\rho_1}$$
 * }
 * }

=1====================
 * {| style="bgcolor:white" cellpadding=5


 * align="center" | $$\frac{T_2}{T_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\cdot\,\!$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_2}{p_1} \right )^\frac {\gamma-1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\left (\frac{V_1}{V_2} \right )^{(\gamma-1)}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{\rho_2}{\rho_1} \right )^{(\gamma - 1)}$$
 * align="center" | $$\frac {p_2} {p_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{T_2}{T_1} \right )^\frac {\gamma}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\cdot\,\!$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\left (\frac{V_1}{V_2} \right )^{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{\rho_2}{\rho_1} \right )^{\gamma}$$
 * align="center" | $$\frac{V_2}{V_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{T_1}{T_2} \right )^\frac {1}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_1}{p_2} \right )^\frac {1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\cdot\,\!$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{\rho_1}{\rho_2}$$
 * align="center" | $$\frac{\rho_2}{\rho_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{T_2}{T_1} \right )^\frac {1}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_2}{p_1} \right )^\frac {1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{V_1}{V_2}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\cdot\,\!$$
 * }
 * align="center" | $$\frac{V_1}{V_2}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\cdot\,\!$$
 * }
 * }

=2====================

Table of isentropic relations for an ideal gas

 * {| style="bgcolor:white" cellpadding=5


 * align="center" | $$\frac {p_2} {p_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{T_2}{T_1} \right )^\frac {\gamma}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{\rho_2}{\rho_1} \right )^{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\left (\frac{V_1}{V_2} \right )^{\gamma}$$
 * align="center" | $$\frac{T_2}{T_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_2}{p_1} \right )^\frac {\gamma-1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{\rho_2}{\rho_1} \right )^{(\gamma - 1)}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\left (\frac{V_1}{V_2} \right )^{(\gamma-1)}$$
 * align="center" | $$\frac{\rho_2}{\rho_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{T_2}{T_1} \right )^\frac {1}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_2}{p_1} \right )^\frac {1}{\gamma}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{V_1}{V_2}$$
 * align="center" | $$\frac{V_2}{V_1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{T_1}{T_2} \right )^\frac {1}{\gamma-1}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$\frac{\rho_1}{\rho_2}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_1}{p_2} \right )^\frac {1}{\gamma}$$
 * }
 * align="center" | $$\frac{\rho_1}{\rho_2}$$
 * align="center" | $$=\,\!$$
 * align="center" | $$ \left (\frac{p_1}{p_2} \right )^\frac {1}{\gamma}$$
 * }
 * }