up::[[Combustion]] https://www.youtube.com/watch?v=rUBXCn9TSas We need to make the following assumptions to formulate the adiabatic flame temperature: - Chemical reactions happen in gaseous state - All gases are perfect gases - "Calorically perfect gas" means [[Specific heat]]s $c_p$ and $c_v$ can be treated as constant instead of a function of temperature - Chemical process occur between equilibrium states ## 1. Some intro To generalize we write chemical reaction like this: $\sum_{i=1}^{N}\ce{n_i^'m_i->}\sum_{i=1}^{N}\ce{n_i^{''}m_i}$ Note all reactants and products are on both sides. [[Enthalpy of reaction]] is $Q_p=\Delta H = H_{reactants}-H_{products}$ $\displaylines{Q_p = \sum_{i=1}^N n_i^{''}\left[{\Delta_{f}}_{STP}H^{\ominus} + \left(h_f(T)-h_{fSTP}^{\ominus}\right)\right]_{products}- \\ \sum_{i=1}^N n_i^{'}\left[{\Delta_{f}}_{STP}H^{\ominus} + \left(h_f(T)-h_{fSTP}^{\ominus}\right)\right]_{reactants}}$ if you set $Q_p=0$ (since it is adiabatic) which means $H_{reactants}=H_{products}$ If we assume pressure is also constant you can set the change in sensible enthalpy of the products to $c_p \Delta T$ and calculate the adiabatic flame temperature. ## 2. Adiabatic Flame temperature In order for a reaction to produce high adiabatic flame temperature (i.e. combustion) i.e. the sensible enthalpy of the products $\left(h_f(T)-h_{fSTP}^{\ominus}\right)$ to be high: - The standard enthalpy of the products needs to be a large negative value. i.e the combustion should produce reactants which are stable i.e. stoichiometric reaction - The standard enthalpy of the reactants should be high - especially the fuel if the oxidizer is oxygen - The sensible enthalpy of the reactants is low (the reactants are at much lower temperature than the products) ## 3. Non-stoichiometric conditions At non-stoichiometric conditions, excess fuel or oxidizer remains and it needs to be raised to the same temperature as the products (increase in sensible enthalpy). Hence non-stoichiometric reactions produce lower temperatures than stoichiometric reactions. Note: fuels tend to have higher $c_p$ compared to oxidizers. hence the slope of the curve tends to be steeper on the fuel rich side compared to the oxygen rich side in this [[Mixture Ratio]] vs flame temperature curve ![[temp_vs_mr.png]] Tools like NASA [[CEA]] and STANJAN can be used to calculate adiabatic flame temperature for various reactions. ## 4. Impact of Pressure Pressure affects the composition of products of combustion (proportion of stable and unstable products) and hence affects the adiabatic flame temperature. This effect is generally small. https://www.researchgate.net/publication/338157321_The_adiabatic_flame_temperature_and_laminar_flame_speed_of_methane_premixed_flames_at_varying_pressures