Thermochemistry

Learning Objectives

  • Distinguish heat from temperature, define system and surroundings, and apply a consistent sign convention for energy transfer.
  • Relate enthalpy to H=U+pVH=U+pV and interpret exothermic and endothermic processes using reaction-energy changes.
  • Calculate sensible heat and calorimeter energy balances using heat capacity, specific heat capacity, mass, temperature change, and stated calorimeter constants.
  • Apply Hess's law and standard enthalpies of formation to balanced reactions while preserving coefficients, physical states, signs, and units.
  • Connect thermochemistry to civil-engineering materials and processes while separating stated exercise inputs from measured or reference data.

Heat (qq)

Energy transferred across a system boundary because of a temperature difference. In this lesson, q>0q>0 means heat enters the chosen system and q<0q<0 means heat leaves it.

Temperature

A measure related to the thermal state of matter that determines the direction of spontaneous heat transfer between bodies in thermal contact. Temperature is not the same thing as the amount of heat transferred.

Heat and Temperature Are Different Quantities

Temperature describes thermal state; heat is energy transferred because of a temperature difference. A large cool body can contain more internal energy than a small hot body.

Temperature
  • A state variable measured on a temperature scale
  • Does not by itself specify how much energy an object gains or loses
  • Affects the direction of spontaneous heat transfer
Heat transfer
  • Energy crossing the system boundary because of a temperature difference
  • Positive here when energy enters the chosen system
  • Stops being 'heat' after transfer; it contributes to the system's internal-energy change

System, Surroundings, and Sign Convention

Define the system before assigning a sign. The surroundings are everything outside that boundary. With the chemistry sign convention used here, energy transferred as heat into the system gives q>0q>0; heat transferred out gives q<0q<0. For pressure-volume work, this lesson uses ΔU=q+w\Delta U=q+w, where w>0w>0 means work is done on the system.

Thermochemistry in Engineering

Thermochemistry is the study of heat transfer during chemical reactions and physical changes. For civil engineers, this is critical for understanding the heat of hydration in mass concrete (which can cause severe thermal cracking), combustion processes, and the thermal properties of building materials for energy efficiency.

Enthalpy (ΔH\Delta H)

Enthalpy (HH)

A thermodynamic state function defined by H=U+pVH=U+pV. For a process at constant pressure in a closed system where pressure-volume work is the only work mode, the heat transferred to the system equals the enthalpy change: qp=ΔHq_p=\Delta H.

Enthalpy Definition

Enthalpy is a state function defined from internal energy, pressure, and volume.

H=U+pVH=U+pV

Variables

SymbolDescriptionUnit
HHEnthalpy-
UUInternal energy-
ppPressure-
VVVolume-

Exothermic Reaction

A reaction where heat is released from the system to the surroundings (ΔH<0\Delta H < 0). Examples include the hydration of cement and combustion of fuels.

Endothermic Reaction

A reaction where heat is absorbed by the system from the surroundings (ΔH>0\Delta H > 0). Examples include melting ice or the thermal decomposition of limestone.

Exothermic and Endothermic Energy Profiles

Compare initial and final enthalpy levels. Activation barriers affect reaction rate but do not change the sign of the overall enthalpy difference between products and reactants.

Exothermic process
  • Products lie at lower enthalpy than reactants
  • ΔH < 0 for the chosen reaction as written
  • Energy is transferred from the reacting system to the surroundings
Endothermic process
  • Products lie at higher enthalpy than reactants
  • ΔH > 0 for the chosen reaction as written
  • Energy is transferred from the surroundings into the reacting system

Interactive Simulation

Use the simulation below to explore the differences between exothermic and endothermic reactions and visualize energy changes.

Calorimetry Simulator (Quenching Steel)

Steel Properties (Hot)

500 g
200 °C

Water Properties (Cold)

1000 g
20 °C

Equilibrium Results

Final Temperature ($T_f$)20.00 °C
Heat Transferred ($q$)40500 J
−qsteel=qwater-q_{steel} = q_{water}
−(mscsΔTs)=mwcwΔTw-(m_{s}c_{s}\Delta T_{s}) = m_{w}c_{w}\Delta T_{w}
−(500)(0.450)(Tf−200)=(1000)(4.184)(Tf−20)-(500)(0.450)(T_f - 200) = (1000)(4.184)(T_f - 20)
Tf=20.00∘CT_f = 20.00 ^\circ\text{C}

Calorimetry and Heat Capacity

Measurement of Heat Flow

Calorimetry is the experimental measurement of heat flow. The core principle is the conservation of energy: heat lost by one part of an isolated system must equal the heat gained by another part.

Specific Heat Formula

Calculates the amount of heat transferred based on mass, specific heat, and temperature change.

q=mcΔTq = mc\Delta T

Variables

SymbolDescriptionUnit
qqHeat transferredJ
mmMassg
ccSpecific heat capacityJ/(g⋅∘C)\text{J}/(\text{g}\cdot^\circ\text{C})
ΔT\Delta TChange in temperature (Tfinal−TinitialT_{\text{final}} - T_{\text{initial}})∘C^\circ\text{C}

Reference Values Versus Exercise Inputs

Water near ordinary laboratory conditions is often modeled with a specific heat near 4.184 J/(g⋅∘C)4.184\,\text{J}/(\text{g}\cdot^\circ\text{C}), but reference values vary with temperature and state. Concrete does not have one universal specific heat: mixture proportions, moisture, density, temperature, and test method matter. When a problem states a value such as 0.880 J/(g⋅∘C)0.880\,\text{J}/(\text{g}\cdot^\circ\text{C}), treat it as an exercise input unless a measured or cited material value is supplied.

Calorimeter Energy Accounting

Choose a system boundary and account for every heat-capacity term included by the model. The measured temperature change links the reacting system to the solution and calorimeter.

1
Reaction or process: unknown heat to be inferred
2
Solution/sample: q = mcΔT when specific heat is treated as constant
3
Calorimeter hardware: q_cal = C_calΔT when its heat capacity is included
4
Energy balance: q_reaction + q_solution + q_cal ≈ 0 for the chosen insulated model

Heat Capacity (CC)

The heat required to change the temperature of an object or calorimeter by one temperature unit under the stated conditions. Heat capacity is an extensive property and has units such as J/K.

Heat Capacity From Mass and Specific Heat

For a material treated as having constant specific heat over the temperature interval.

C=mcC=mc

Variables

SymbolDescriptionUnit
CCHeat capacity of the sampleJ/K\text{J/K}
mmSample mass-
ccSpecific heat capacity-

Ideal Calorimeter Energy Balance

For a sufficiently insulated calorimeter model, energy gained and lost by included parts sums approximately to zero.

qrxn+qsample+qcal≈0q_{\text{rxn}}+q_{\text{sample}}+q_{\text{cal}}\approx0

Variables

SymbolDescriptionUnit
qrxnq_{\text{rxn}}Heat associated with the reaction or process for the chosen system-
qsampleq_{\text{sample}}Heat gained or lost by the solution or sample-
qcalq_{\text{cal}}Heat gained or lost by calorimeter hardware when included-

Hess's Law

Hess's Law Principles

In many cases, it is impossible to measure the ΔH\Delta H of a reaction directly. Hess's Law states that if a reaction is carried out in a series of steps, ΔH\Delta H for the overall reaction equals the sum of the enthalpy changes for the individual steps. This is because enthalpy is a state function (depends only on the current state, not the path taken).

Standard Enthalpy of Reaction

Calculates the overall enthalpy change of a reaction using standard enthalpies of formation.

ΔHrxn∘=∑nΔHf∘(products)−∑mΔHf∘(reactants)\Delta H^\circ_{\text{rxn}} = \sum n \Delta H_f^\circ (\text{products}) - \sum m \Delta H_f^\circ (\text{reactants})

Variables

SymbolDescriptionUnit
ΔHrxn∘\Delta H^\circ_{\text{rxn}}Standard enthalpy change of the reaction-
ΔHf∘\Delta H_f^\circStandard enthalpy of formationkJ/mol\text{kJ/mol}
n,mn, mStoichiometric coefficients from the balanced equation-

Standard Enthalpy of Formation (ΔHf∘\Delta H_f^\circ)

The standard enthalpy change for forming exactly one mole of a substance from its constituent elements in their reference standard states under the specified standard conditions. By convention, an element in its reference standard state has ΔHf∘=0\Delta H_f^\circ=0.

Hess's Law: Direct and Multistep Paths

Enthalpy is a state function, so any valid set of reaction steps that sums to the target reaction must give the same overall ΔH.

Target reaction
  • Write the balanced target reaction with physical states
  • The required quantity is the enthalpy difference between the same initial and final states
Equivalent reaction path
  • Reverse a step → reverse the sign of ΔH
  • Multiply a reaction by a factor → multiply ΔH by the same factor
  • Add the adjusted steps and cancel intermediates before summing ΔH values

System Boundaries and Civil-Engineering Applications

  • Mass concrete: cement hydration releases heat. Temperature rise and thermal gradients depend on cementitious materials, member dimensions, placement temperature, heat transfer, curing, and construction sequence; a single specific-heat value does not define cracking risk.
  • Lime and cement manufacture: decomposition and high-temperature reactions require energy accounting with clearly defined reaction states and reference data.
  • Combustion and building energy: fuel reaction enthalpies support energy balances, but equipment efficiency and heat losses are separate engineering quantities.
  • Materials testing and laboratory work: distinguish a property taken from a reference source from a value measured for the actual specimen or mixture.

Reaction Enthalpy Depends on the Reaction as Written

Before using tabulated standard formation enthalpies, balance the chemical equation and retain physical states. Reversing a reaction reverses ΔH\Delta H; multiplying every coefficient by a factor multiplies ΔH\Delta H by the same factor. Report whether an answer is per mole of reaction, per mole of a named species, or for the stated batch.

Thermodynamics vs Thermochemistry

Thermodynamics Relation

Thermochemistry is technically a branch of thermodynamics. In engineering thermodynamics, we frequently refer to the First Law of Thermodynamics, which relates internal energy change to heat (qq) and work (ww).

First Law of Thermodynamics

The change in internal energy of a closed system.

ΔU=q+w\Delta U = q + w

Variables

SymbolDescriptionUnit
ΔU\Delta UChange in internal energy of the system-
qqHeat added to the system-
wwWork done on the system-
Key Takeaways
  • Heat is energy transfer caused by a temperature difference; temperature is a state variable and is not synonymous with heat content.
  • Enthalpy is H=U+pVH=U+pV; under the stated constant-pressure, pressure-volume-work conditions, qp=ΔHq_p=\Delta H.
  • In calorimetry, define the system boundary and include every heat-capacity term used by the model before applying energy conservation.
  • Hess's law works because enthalpy is a state function; reversing or scaling a reaction changes the associated ΔH\Delta H in the same algebraic way.
  • Formation enthalpy calculations require balanced equations, physical states, consistent units, and clear distinction between reference data and exercise assumptions.

References