Thermodynamic Terms and First Law

System, Surrounding, and Boundary

A system is any portion of the universe that is under study or observation. The rest of the universe outside the system is called the surroundings. In practice, the system consists of a specific amount of one or more substances — for example, one mole of oxygen confined in a cylinder fitted with a piston, or a cup of water on a table. Everything outside the defined system — the cylinder walls, the piston, the air, the table — belongs to the surroundings.

Gas in a cylinder: The gas is the system; the cylinder, piston, and everything outside are the surroundings

Cup of water: The water is the system; the surrounding air, the table it rests on, and the room are the surroundings

Chemical reaction: The reacting mixture (e.g., Zn and CuSO₄ solution in a flask) is the system; the flask, the air, and the laboratory are the surroundings

The boundary is the real or imaginary surface that separates the system from the surroundings. A boundary can be a physical wall — like the walls of a cylinder or the glass of a beaker — or it can be an imaginary dividing surface with no material existence. The boundary defines where the system ends and the surroundings begin, and it is across this boundary that heat and work are exchanged between the system and its surroundings.

State Functions

Every system exists in a particular condition called its state, defined by measurable properties such as temperature, pressure, and volume. When a process acts on the system, its state changes. The condition before the change is the initial state and the condition after the change is the final state. The difference between the final and initial values of any property is called the change in that property.

$$\Delta T = T_2 - T_1$$

Calculates the change in temperature between two states of a system

$\Delta T$=Change in temperature(K or °C)

$T_2$=Final temperature(K or °C)

$T_1$=Initial temperature(K or °C)

A state function is a macroscopic property of a system that has a definite value for any given state. The change in a state function depends only on the initial and final states — it is entirely independent of the path taken to get from one state to the other. By convention, state functions are represented by capital letters, such as P (pressure), T (temperature), V (volume), E (internal energy), and H (enthalpy).

$$\Delta V = V_2 - V_1$$

Calculates the change in volume between two states of a system

$\Delta V$=Change in volume(L or m³)

$V_2$=Final volume(L or m³)

$V_1$=Initial volume(L or m³)

$\Delta V > 0$

→

System has expanded

$\Delta V < 0$

→

System has been compressed

Common State Functions

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Pressure ($P$)

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Temperature ($T$)

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Volume ($V$)

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Internal energy ($E$)

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Enthalpy ($H$)

Internal Energy

The internal energy ($E$) of a system is the sum total of all possible kinds of energies possessed by the particles within it. It includes kinetic energy from the translational, rotational, and vibrational motions of molecules, and potential energy from all attractive forces between particles, including chemical bonds and van der Waals forces. Internal energy is itself a state function, meaning only its change ($\Delta E$) between states is measurable.

Kinetic energy contributions: Translational motion (movement through space), rotational motion (spinning about an axis), and vibrational motion (oscillation of atoms within bonds)

Potential energy contributions: All types of bonds (covalent, ionic, metallic, hydrogen) and intermolecular forces (van der Waals forces, dipole-dipole interactions)

Molecular Motions Contributing to Internal Energy

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All molecules: translational motion

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Diatomic and larger molecules: rotational motion

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Diatomic and larger molecules: vibrational motion

Although it is not possible to measure the absolute value of the internal energy of a system, it is possible to measure the change in internal energy ($\Delta E$) for any change in the state of the system. This is because $\Delta E$ is a state function, and its value depends only on the initial and final states. Energy can be transferred into or out of a system through two fundamental mechanisms: heat and work.

Absolute internal energy cannot be measured: There is no reference point for zero internal energy

Change in internal energy is measurable: $\Delta E = E_2 - E_1$ is determined by the initial and final states alone

Energy transfer occurs via heat and work: These are the only two ways a system exchanges energy with its surroundings

Heat and Work

Heat is the quantity of energy that flows across the boundary of a system during a change in its state, driven by a temperature difference between the system and the surroundings. Heat is denoted by the symbol $q$. Crucially, heat is not a property of a system and is therefore NOT a state function — the amount of heat transferred depends on the path taken.

Positive $q$: Heat is absorbed by the system from the surroundings (energy enters the system)

Negative $q$: Heat is released by the system to the surroundings (energy leaves the system)

Work is a form of energy transfer defined as the product of force and distance ($W = F \times S$). In thermochemistry, the most common type is pressure-volume work, which occurs when a system expands or contracts against an external pressure. For example, when a gas is evolved during a chemical reaction (such as $CaCO_3 + 2HCl \rightarrow CaCl_2 + CO_2 + H_2O$), the gas does work by pushing back the atmosphere. Like heat, work is not a state function.

$$W = -P\Delta V$$

Calculates the pressure-volume work done by a system expanding against (or being compressed by) an external pressure

$W$=Work done (negative when done by the system, positive when done on the system)(J or kJ)

$P$=External pressure acting on the system(Pa or atm)

$\Delta V$=Change in volume of the system ($V_f - V_i$)(L or m³)

$\Delta V > 0$ (expansion)

→

$W$ is negative — the system does work on the surroundings

$\Delta V < 0$ (compression)

→

$W$ is positive — the surroundings do work on the system

$\Delta V = 0$ (constant volume)

→

$W = 0$ — no pressure-volume work is done

Positive $W$: Work is done on the system by the surroundings (energy enters the system, e.g., compression)

Negative $W$: Work is done by the system on the surroundings (energy leaves the system, e.g., expansion)

First Law of Thermodynamics

The first law of thermodynamics states that energy can neither be created nor destroyed, but can only be changed from one form to another. This is also known as the law of conservation of energy. A system cannot create or destroy energy — it can only exchange energy with its surroundings through heat and work. The total energy of the system and its surroundings always remains constant.

$$\Delta E = q + w$$

States that the change in a system's internal energy equals the net heat absorbed plus the net work done on the system

$\Delta E$=Change in internal energy of the system(J or kJ)

$q$=Heat absorbed by the system (positive if absorbed, negative if released)(J or kJ)

$w$=Work done on the system (positive if done on, negative if done by)(J or kJ)

$\Delta E > 0$

→

System gains energy overall

$\Delta E < 0$

→

System loses energy overall

When the pressure-volume work is the only form of work, the first law becomes $\Delta E = q - P\Delta V$. If the volume of the system is held constant (as in a sealed rigid container), then $\Delta V = 0$ and no pressure-volume work is done. Under these conditions, the entire energy change of the system is due to heat transfer alone.

$$\Delta E = q_v$$

At constant volume, the change in internal energy equals the heat absorbed by the system

$\Delta E$=Change in internal energy(J or kJ)

$q_v$=Heat absorbed at constant volume(J or kJ)

Constant volume condition: No expansion or compression occurs, so $P\Delta V = 0$

Practical significance: Reactions carried out in sealed containers (e.g., bomb calorimeters) occur at constant volume

Enthalpy

Enthalpy ($H$) is a thermodynamic property of a system defined as the sum of its internal energy and the product of its pressure and volume. Like internal energy, enthalpy is a state function and is measured in joules. While the absolute value of enthalpy cannot be determined, the change in enthalpy ($\Delta H$) for a process can be measured and is extremely useful in chemistry.

$$H = E + PV$$

Defines enthalpy as internal energy plus the pressure-volume product of the system

$H$=Enthalpy of the system(J or kJ)

$E$=Internal energy of the system(J or kJ)

$P$=Pressure of the system(Pa or atm)

$V$=Volume of the system(L or m³)

When a system absorbs heat at constant pressure, part of the energy increases the internal energy and the rest is used to do pressure-volume work as the system expands. The change in enthalpy ($\Delta H$) accounts for both effects. By combining the first law of thermodynamics with the enthalpy definition and applying the constant-pressure condition, it can be shown that the change in enthalpy equals the heat of reaction at constant pressure.

$$\Delta H = q_p$$

At constant pressure, the change in enthalpy equals the heat exchanged by the system

$\Delta H$=Change in enthalpy of the system(J or kJ)

$q_p$=Heat absorbed or released at constant pressure(J or kJ)

Most reactions occur at constant pressure: Open beakers and flasks are at atmospheric pressure, so $\Delta H = q_p$ is more commonly used than $\Delta E$

Derivation: From $\Delta E = q - P\Delta V$ and $\Delta H = \Delta E + P\Delta V$, substituting gives $\Delta H = q - P\Delta V + P\Delta V = q$ at constant pressure

Chemical processes are classified by the sign of $\Delta H$. In an exothermic process, the system releases heat to the surroundings and $\Delta H$ is negative. In an endothermic process, the system absorbs heat from the surroundings and $\Delta H$ is positive. The magnitude of $\Delta H$ tells us how much energy is transferred during the process.

Exothermic ($\Delta H < 0$): Products have lower enthalpy than reactants — energy is released to the surroundings

Endothermic ($\Delta H > 0$): Products have higher enthalpy than reactants — energy is absorbed from the surroundings

Exothermic vs Endothermic

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Exothermic: $H_{\text{products}} < H_{\text{reactants}}$, $\Delta H$ is negative, surroundings get warmer

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Endothermic: $H_{\text{products}} > H_{\text{reactants}}$, $\Delta H$ is positive, surroundings get cooler

The change in enthalpy and the change in internal energy are related by $\Delta H = \Delta E + P\Delta V$. For gaseous reactions where the number of moles changes, the $P\Delta V$ term is significant. Using the ideal gas equation, $P\Delta V$ can be expressed in terms of the change in moles of gas. For reactions involving only liquids and solids, volume changes are negligible, so $\Delta H \approx \Delta E$.

$$P\Delta V = \Delta nRT$$

Expresses pressure-volume work in terms of the change in moles of gas during a reaction at constant temperature

$P\Delta V$=Pressure-volume work done by the system(J)

$\Delta n$=Change in moles of gas (moles of gaseous products minus moles of gaseous reactants)(mol)

$R$=Universal gas constant ($8.314 \text{ J K}^{-1} \text{ mol}^{-1}$)(J K⁻¹ mol⁻¹)

$T$=Absolute temperature(K)

$\Delta n = 0$

→

$P\Delta V = 0$, so $\Delta H = \Delta E$

Only solids and liquids involved

→

$\Delta V \approx 0$, so $\Delta H \approx \Delta E$

For gases: Calculate $\Delta n = n_{\text{gaseous products}} - n_{\text{gaseous reactants}}$ and use $\Delta H = \Delta E + \Delta nRT$

For solids and liquids: Volume changes are negligible, so $\Delta H$ and $\Delta E$ are approximately equal

Heat Capacity and Calorimetry

The heat capacity ($C$) of a body or system is the quantity of heat required to change its temperature by 1 kelvin. When the mass of the substance is specified, the specific heat ($s$) is used — the heat required to raise the temperature of 1 gram of a substance by 1 kelvin. The product of mass and specific heat gives the total heat capacity of a system.

$$q = ms\Delta T$$

Calculates the heat absorbed or released by a substance using its mass, specific heat, and temperature change

$q$=Heat energy transferred (positive if absorbed, negative if released)(J or kJ)

$m$=Mass of the substance(g)

$s$=Specific heat capacity(J g⁻¹ K⁻¹)

$\Delta T$=Change in temperature ($T_f - T_i$)(K)

$C = ms$

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Total heat capacity can replace the product $ms$, giving $q = C\Delta T$

Key Heat Capacity Relationships

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$q = ms\Delta T$ (using mass and specific heat)

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$q = C\Delta T$ (using total heat capacity, where $C = ms$)

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Specific heat of water = $4.2 \text{ J g}^{-1} \text{ K}^{-1}$

Calorimeter Types

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Glass calorimeter: Insulated container with thermometer and stirrer — used for reactions in solution (neutralization, dissolution)

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Bomb calorimeter: Strong steel vessel with electrical ignition — used for combustion reactions at constant volume

Calorimetry is the experimental technique for measuring the heat absorbed or released during a chemical reaction. A calorimeter is an insulated vessel that prevents heat exchange with the surroundings. Reactants are mixed inside the calorimeter in stoichiometric amounts, and the temperature change is recorded before and after the reaction. Using the temperature change, the mass of the solution, and the specific heat, the quantity of heat transferred can be calculated using $q = ms\Delta T$.

Glass calorimeter procedure: Place reactants in the insulated container, stir continuously, record initial and final temperatures, then calculate $q = ms\Delta T$

Bomb calorimeter procedure: Place a known mass of sample in the steel bomb, pressurize with oxygen (~20 atm), immerse in water, ignite electrically, and record the temperature rise of the surrounding water. Use $q = C\Delta T$ where $C$ is the known heat capacity of the entire calorimeter assembly