Thermochemistry

Most of the world's energy still comes from chemical reactions: burning natural gas, oil, coal and wood. Engineers who design furnaces, boilers, engines and reactors need to know how much heat a reaction releases or absorbs, and how much it takes to heat, melt or boil the materials involved. Thermochemistry provides those numbers.

This chapter covers heat and temperature, specific heat and calorimetry, phase changes, the enthalpy of reaction, Hess's law and standard enthalpies of formation, and applies them to fuel heating values, home heating and industrial energy use.

Energy, heat and the system

Energy is the capacity to do work or transfer heat, measured in joules. Heat (\(q\)) is energy transferred because of a temperature difference; work (\(w\)) is energy transferred by a force acting through a distance, such as a gas pushing a piston. Temperature is not energy: it measures the average kinetic energy of the particles, and it tells you which way heat will flow.

To keep track, chemists divide the world into the system (the reaction or material you are studying) and the surroundings (everything else). The sign convention is from the system's point of view:

• \(q > 0\): heat flows into the system (endothermic, the surroundings cool).
• \(q < 0\): heat flows out of the system (exothermic, the surroundings warm).

The first law of thermodynamics says energy is conserved: the change in a system's internal energy is the heat added minus the work it does, \(\Delta U = q - w\) in the convention engineers usually use. You will study the first law in full in thermodynamics; this chapter focuses on heat.

Specific heat and sensible heat

Heat that changes a material's temperature is called sensible heat. The amount needed is

where \(c\) is the specific heat capacity in J/(g·K) or kJ/(kg·K). A change of 1 K equals a change of 1 °C, so either can be used for \(\Delta T\). Water has an unusually high specific heat, 4.184 J/(g·K), which is why it is the standard heat-transfer fluid in boilers and cooling systems, and why lakes moderate the climate around them. Typical values: steel about 0.49, aluminium 0.90, concrete about 0.88, air (constant pressure) 1.005, and engine oil about 2.0 J/(g·K).

Calorimetry

A calorimeter measures heat by watching a temperature change in a well-insulated container. If no heat is lost, the heat lost by hot objects equals the heat gained by cold ones: \(\sum q = 0\).

Phase changes and latent heat

When a substance melts, boils or condenses, it absorbs or releases heat without changing temperature, because the energy goes into breaking or forming the bonds between molecules. This is latent heat:

For water, the latent heat of fusion (melting) is 334 kJ/kg and the latent heat of vaporization at 100 °C is 2257 kJ/kg. Boiling a kilogram of water takes more than five times as much energy as heating it from 0 °C to 100 °C.

Latent heat is what makes steam such an effective way to carry energy around a plant: condensing 1 kg of steam delivers 2257 kJ at a constant temperature, ideal for heating process vessels evenly. It is also why steam burns are so severe, and why evaporative coolers and cooling towers work so well.

Enthalpy of reaction

Most reactions happen at constant pressure, open to the atmosphere or in a process vessel. The heat absorbed or released at constant pressure is the change in enthalpy, \(\Delta H\). For an exothermic reaction \(\Delta H < 0\); for an endothermic one \(\Delta H > 0\).

A thermochemical equation attaches \(\Delta H\) to a balanced equation, per mole of reaction as written:

Three rules follow from enthalpy being a state function (it depends only on the current state, not on how it was reached):

• \(\Delta H\) scales with the amount: burning 2 mol of methane releases 1780 kJ.
• Reversing a reaction reverses the sign of \(\Delta H\).
• Physical states matter: forming water vapour instead of liquid releases less heat, because vapour still holds its latent heat.

Hess's law

Because enthalpy is a state function, the enthalpy change for a reaction is the same whether it happens in one step or several. This is Hess's law, and it lets you calculate \(\Delta H\) for reactions that are hard to measure directly by combining ones that are easy to measure.

Standard enthalpies of formation

The most practical form of Hess's law uses tabulated standard enthalpies of formation, \(\Delta H_f^\circ\): the enthalpy change when one mole of a compound forms from its elements in their standard states (at 25 °C and 1 bar). Elements in their standard states, such as O₂(g), N₂(g) and C(graphite), have \(\Delta H_f^\circ = 0\) by definition. Then for any reaction:

Some values in kJ/mol: CO₂(g) −393.5, H₂O(l) −285.8, H₂O(g) −241.8, CH₄(g) −74.8, C₃H₈(g) −103.8, CO(g) −110.5, NH₃(g) −45.9, CaCO₃(s) −1207.6, CaO(s) −634.9.

Higher and lower heating values

Fuel energy is quoted two ways. The higher heating value (HHV) assumes the water in the flue gas condenses to liquid, recovering its latent heat. The lower heating value (LHV) assumes it leaves as vapour.

Estimating with bond energies

When formation data are missing, \(\Delta H\) can be estimated from average bond energies: energy is absorbed to break bonds in the reactants and released when bonds form in the products. For methane combustion, breaking four C–H bonds (413 kJ each) and two O=O bonds (495 kJ each) absorbs 2642 kJ, while forming two C=O bonds (799 kJ each) and four O–H bonds (463 kJ each) releases 3450 kJ, giving \(\Delta H \approx -808\) kJ. That is within 1% of the true value for gaseous water, −802 kJ. Bond energies are averages, so the estimate is usually good to about 10%.

Adiabatic flame temperature

If a fuel burns with no heat lost, all the heat of combustion goes into warming the products. The temperature they reach is the adiabatic flame temperature, the upper limit for a furnace or engine, and it is set by an energy balance: heat released = heat absorbed by the products.

Flame temperature matters for equipment life and emissions. Nitrogen oxides (NOₓ), which contribute to smog, form rapidly above about 1800 K, so low-NOₓ burners deliberately spread out or cool the flame.

Energy in engineering practice