Posts Tagged ‘internal combustion engine’

Thermodynamics in Mechanical Engineering, Part IV, Stoichiometry

Sunday, December 27th, 2009

     Last week we talked about an area of thermodynamics that concerns refrigeration cycles as presented through the example of an air conditioner.  This week, we’ll learn about stoichiometry, which is concerned with the math behind chemical reactions, like those that take place during the burning of fuels.

     During the combustion process, heat energy is released from a fuel when the combustible elements in the fuel combine with oxygen.  This is known as oxidation, or in common everyday language as burning. The most important thing to remember about oxidation is that it obeys the first law of thermodynamics.  That is, mass cannot be created or destroyed.  In a chemical reaction like combustion, particles of fuel and air are rearranged in space and then combine to form different substances.  However, despite the rearranging, the mass that goes into the reaction must equal the mass that comes out.  This conservation of mass is the basis of stoichiometry.

     For example, if pure carbon (represented by the chemical symbol “C”) is burned in pure oxygen (O2), you can represent the combustion process as:

C + O2 → CO2

     This is chemistry shorthand for representing how carbon and oxygen combine during burning to form carbon dioxide (CO2).  The elements to the left of the arrow are known as “reactants” and the elements to the right are known as “products.”  In stoichiometry, the mass of the reactants must equal the mass of the products.  But, how do we quantify the mass of reactants and products?  Now this is where it gets a little weird.

     To make use of our chemistry shorthand above, we have to consider something called moles.  No, these aren’t the little furry creatures that tunnel under your lawn and eat your tulip bulbs.  In stoichiometry a mole is considered to be 6.02×1023 molecules of a substance.  That is 602,000,000,000,000,000,000,000 molecules!

     Okay, so we have one heck of a lot of molecules in a mole.  So, what does that have to do with figuring out how much mass we are dealing with in the combustion process?  Well, in order to make moles work for us, we have to take into consideration the differing molecular weights of substances.  Molecular weight is the number of grams (g) of mass that are contained within one mole of a substance, like the element carbon in our example above. To help make stoichiometry more workable, scientists created a table that provides the molecular weight of all known chemical elements.  This table is known as the Periodic Table of Elements, or the “Periodic Table” for short.

     Now going back to our example above, if we know from the Periodic Table that carbon has a molecular weight of 12 g per mole and oxygen has a molecular weight of 16 g per mole, then how many grams of carbon dioxide do we get by burning carbon in pure oxygen?  The combustion process can be represented by this equation:

C + O2 → CO2

(12 g/mole) × (1mole of carbon) + (16 g/mole) × (2 moles of oxygen)

= 44 g of carbon dioxide

     This is a fairly straightforward example of how stoichiometry works.  In reality, things can get far more complicated.  In a power plant for example, fuels like coal contain substances in addition to carbon, such as hydrogen and sulfur, and they, too, must be factored into the stoichiometric accounting system. 

     To further complicate things, fuels are usually burned in air, rather than pure oxygen.  Air, too, contains substances other than oxygen, including nitrogen, argon, and molecules of water.  These other substances’ presence in fuel and air make the combustion process more challenging to account for, because they all get mixed together, and they can combine into all sorts of other substances.  Despite these complicating factors, the first law of thermodynamics must be obeyed, so the balancing act is still the same:  mass of the reactants must equal the mass of the products.

     Once mechanical engineers use stoichiometry to figure out what’s going in and coming out of the combustion process, they can then use the data provided by chemical analysis of the fuel to calculate the heat energy that is released.  They can also calculate the air required for proper combustion.  This helps them to design things capable of delivering enough fuel and air to meet the heat input requirements for a diversity of power cycles, from the engine in your car to the coal fired power plant supplying electricity for your home.

     Next week, we’ll talk about psychrometric analysis.  No, this has nothing to do with psychiatry.  Psychrometrics involves the analysis of gas and vapor mixtures like air and water.