In general, for polyester, the melting temperature \(T_m\), pyrolysis temperature \(T_p\), and combustion temperature \(T_c\) follow a specific order based on the thermal behavior of the material:
Step 1: Understanding the melting point \(T_m\). The melting point \(T_m\) is the temperature at which the solid polyester fiber transitions to a liquid phase. This is typically the lowest of the three temperatures because the polymer melts before it undergoes further degradation.
Step 2: Pyrolysis temperature \(T_p\). Pyrolysis is the decomposition of the polyester under heat in the absence of oxygen. It generally occurs at a temperature higher than the melting point but lower than the combustion temperature.
Step 3: Combustion temperature \(T_c\). Combustion occurs at a temperature higher than both the melting and pyrolysis temperatures, as it involves the complete burning of the polyester in the presence of oxygen.
Thus, the correct order of temperatures is \(T_m<T_p<T_c\).