- The First Law of Thermodynamics states that energy can neither be created nor destroyed but can only be converted from one form to another.
- According to this law, the total energy of the system and surroundings remains constant during any physical or chemical change.
- When a system exchanges heat or work with surroundings, its internal energy changes.
- If heat (Q) is supplied to the system and work (W) is done on the system, the internal energy increases.
- The mathematical expression of the first law is
ΔU = Q + W. - For infinitesimal changes, the first law is written as
dU = dQ + dW. - For special processes:
• Isothermal process: ΔU = 0
• Adiabatic process: Q = 0 and −ΔU = W
• Isochoric process: ΔV = 0 and ΔU = Qᵥ
• Isobaric process: Qₚ = ΔU + PΔV.
Definitions [41]
Definition: Thermodynamics
The study of heat and other forms of energy entering or leaving the system due to physical or chemical transformations is called thermodynamics.
Define Intensive property.
A property which is independent of the amount of matter in a system is called an intensive property.
e.g., pressure, temperature.
Define isobaric process.
In isobaric process the pressure remains constant during the transformation.
Define Closed system.
A closed system is one that is able to interchange energy but not matter with its surroundings.
Define Adiabatic process.
A process in which there is no exchange of heat between the system and surroundings is an adiabatic process, or Q = 0.
Define the extensive properties.
A property that depends on the amount of matter present in a system is called an extensive property.
Example: mass, volume.
Define a state function.
A property that depends on the state of a system and is independent of the path taken to reach that state is called a state function.
Define the quasi-static process.
A quasi-static process is an infinitely slow process in which the system changes its variables (P, V, T) so slowly such that it remains in thermal, mechanical, and chemical equilibrium with its surroundings throughout.
Define one calorie.
One calorie is defined as the amount of heat energy needed to raise the temperature of one gram of water by one degree Celsius at a pressure of one atmosphere.
Define the internal energy of the system.
The internal energy of a thermodynamic system is the sum of kinetic and potential energies of all the molecules of the system with respect to the center of mass of the system.
Definition: Intensive Variables
The thermodynamic state variables that do not depend on the size of the system (e.g., pressure, temperature) are called intensive variables.
Definition: Thermodynamic State Variables
The specific values of macroscopic variables that completely describe every equilibrium state of a thermodynamic system are called thermodynamic state variables.
Definition: Extensive Variables
The thermodynamic state variables that depend on the size of the system (e.g., internal energy, volume) are called extensive variables.
Define enthalpy of combustion.
The heat of combustion of a substance is defined as “The change in enthalpy of a system when one mole of the substance is completely burnt in excess of air or oxygen”. It is denoted by ∆HC.
Define enthalpy of neutralization.
The enthalpy of neutralization is defined as the change in enthalpy of the system when one gram equivalent of an acid is neutralized by one gram equivalent of a base or vice versa in dilute solution.
\[\ce{H^+_{(aq)} + OH^-_{(aq)} -> H2O_{(l)}}\] = 57.32 kJ
Definition: Enthalpy
The total heat content of a system at constant pressure is known as enthalpу.
ΔH = ΔU + PΔV
At constant pressure: ΔH = qp (heat exchanged at constant pressure).
Define enthalpy.
Enthalpy of a system is sum of internal energy of a system and the energy equivalent to PV work.
H = U + PV
Define the Enthalpy of vaporization.
Enthalpy of vaporization is the enthalpy change accompanying the vaporization of one mole of liquid without changing its temperature at constant pressure.
Define the Enthalpy of atomization.
The enthalpy change accompanying the dissociation of one mole of gaseous substance into atoms is called enthalpy of atomization.
Define the Enthalpy of sublimation.
Enthalpy of sublimation is the enthalpy change for the conversion of one mole of solid directly into vapour at constant temperature and pressure.
Define the enthalpy of freezing.
The enthalpy change that accompanies the solidification of one mole of a liquid into a solid at constant temperature and pressure is called the enthalpy of freezing.
Define the Bond enthalpy.
The enthalpy change required to break a particular covalent bond in one mole of the gaseous molecule to produce gaseous atoms and/or radicals is called bond enthalpy.
Define the Enthalpy of ionisation.
Enthalpy of ionization is the enthalpy change accompanying the removal of an electron from one mole of a gaseous atom.
Define standard enthalpy of formation.
The standard enthalpy of formation of a compound is the enthalpy change that accompanies a reaction in which one mole of pure compound in its standard state is formed from its elements in their standard states.
Define the Standard enthalpy of combustion.
The standard enthalpy of combustion of a substance is the standard enthalpy change accompanying a reaction in which one mole of the substance in its standard state is completely oxidised.
Define second law of thermodynamics.
Second law of thermodynamics: In a spontaneous process, the overall entropy of the system and its surroundings grows.
Definition: Gibbs Free Energy
The maximum amount of energy available to a system during a process that can be converted into useful work is called the Gibbs free energy.
It is given as, ΔG = ΔH – TΔS
where,
- ΔG = change in Gibbs energy
- ΔH = change in enthalpy
- ΔS = change in entroру.
Define entropy.
Entropy (S) is defined more precisely as a thermodynamic state function that measures the degree of randomness or disorder of the particles in a system.
Definition: Spontaneous process
A process which occurs on its own without any external influence is called spontaneous process.
Definition: Chemical Transformations
Thermodynamics is concerned with the energy changes in physical and chemical transformations.
Definition: State Function
The property which depends only on the state of the system and not on the path followed is called state function.
Definition: Path functions
The properties which depend on the path followed are called path functions.
Definition: Thermodynamic equilibrium
A system is said to be in thermodynamic equilibrium when its state functions do not change with time is called thermodynamic equilibrium.
Definition: Enthalpy
The sum of internal energy and pressure–volume energy of a system is called enthalpy.
Definition: Bond enthalpy
The enthalpy change required ·to break particular covalent bond in one mole of gaseous molecule to produce gaseous atoms and/or radicals, is called bond enthalpy.
Definition: Enthalpy of vaporization
Enthalpy change accompanying vaporization of one mole of liquid at constant temperature and pressure is called enthalpy of vaporization.
Definition: Enthalpy of sublimation
Enthalpy change for conversion of one mole of solid directly into vapour at constant temperature and pressure is called enthalpy of sublimation.
Definition: Enthalpy of fusion
Enthalpy change accompanying conversion of one mole of solid into liquid at constant temperature and pressure is called enthalpy of fusion.
Definition: Intensive property
A property which is independent of the amount of matter in a system is called intensive property.
Examples: Pressure, temperature, surface tension, viscosity, melting point, boiling point, specific heat.
Definition: Extensive property
A property which depends on the amount of matter present in a system is called an extensive property.
Examples: Mass, volume, internal energy, heat capacity, number of moles.
Definition: Entropy
A measure of molecular disorder or randomness of a system is called entropy.
Formulae [1]
Write the mathematical equation of the first law of thermodynamics for an isochoric process.
By substituting equation W = −pex . ΔV in the equation ΔU = q + W, we get
ΔU = q − pex . ΔV ...(1)
If the reaction is carried out in a closed container so that the volume of the system is constant, then Δ = 0. In such a case, no work is involved.
The equation (1) becomes ΔU = qv
Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.
Theorems and Laws [5]
Write the mathematical equation of the first law of thermodynamics for an isochoric process.
By substituting equation W = −pex . ΔV in the equation ΔU = q + W, we get
ΔU = q − pex . ΔV ...(1)
If the reaction is carried out in a closed container so that the volume of the system is constant, then Δ = 0. In such a case, no work is involved.
The equation (1) becomes ΔU = qv
Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.
Law: First Law of Thermodynamics
Statement:
The net heat energy supplied to a system is equal to the sum of the change in internal energy of the system and the work done by the system. It is based on the law of conservation of energy.
Formula:
Q = ΔU + W
where Q = heat added, ΔU = change in internal energy, W = work done by the system.
Law: Second Law of Thermodynamics
The entropy of the universe keeps increasing and tends to reach a maximum.
Total entropy change:
ΔSuniverse = ΔSsystem + ΔSsurroundings > 0
- ΔStotal > 0 → Process is spontaneous
- ΔStotal < 0 → Process is non-spontaneous
- ΔStotal = 0 → System is at equilibrium
Law: First law of thermodynamics
Law: Second low of thermodynamics
- The Second Law of Thermodynamics states that the total entropy of a system and its surroundings increases in a spontaneous process.
- For a process to be spontaneous, the total entropy change must be positive, given by
ΔSₜₒₜₐₗ = ΔSₛᵧₛ + ΔSₛᵤᵣᵣ > 0. - The entropy change of surroundings is calculated using
ΔSₛᵤᵣᵣ = −ΔH / T (at constant temperature). - If ΔSₜₒₜₐₗ > 0, the process is spontaneous; if ΔSₜₒₜₐₗ < 0, the process is non-spontaneous.
- At equilibrium, the total entropy change is zero, that is
ΔSₜₒₜₐₗ = 0.
Key Points
Key Points: Terms Used in Thermodynamics
Basic Terms:
- System: The specific part of the universe selected for study in thermodynamics
- Surroundings: Everything outside the system
- Boundary: Surface separating system & surroundings
Types of System:
- Open: Matter + Energy exchange (Δm ≠ 0, ΔE ≠ 0)
- Closed: Only Energy exchange (Δm = 0, ΔE ≠ 0)
- Isolated: No exchange (Δm = 0, ΔE = 0)
Properties:
- Extensive: Properties whose magnitude depends on the amount of matter → Mass, Volume
- Intensive: Properties independent of the amount of matter→ Temperature, Pressure
Functions:
- State Function: Depends only on state → P, V, T, U, H, G, S
- Path Function: Depends on path → Heat (q), Work (W)
Thermodynamic Processes:
- Adiabatic: Process in which no heat exchange occurs → dq = 0
- Isothermal: Process carried out at constant temperature → dT = 0
- Isobaric: Process carried out at constant pressure → dP = 0
- Isochoric: Process carried out at constant volume → dV = 0
Other Processes:
- Reversible: Process which occurs infinitely slowly and can be reversed by small changes
- Irreversible: Process which cannot be reversed completely
Key Points: Nature of Heat and Work
- Work is done during expansion or compression against external pressure and is a path function.
- Formula: W = −Pext ΔV
- Heat is the transfer of energy between a system and its surroundings.
- Heat is also a path function (depends on the path followed).
- q > 0 when heat is absorbed by system; q < 0 when heat is released.
- Both heat and work are modes of energy transfer, not state functions.
Key Points: Expression for Pressure–Volume (PV) Work
Work in Isothermal Reversible Process
\[W_{rev}=-2.303nRT\log_{10}\frac{V_2}{V_1}\]
Or equivalently using Boyle's law (at constant T):
\[W_{rev}=-2.303nRT\log_{10}\frac{P_1}{P_2}\]
Where: n = number of moles; R = gas constant; T = absolute temperature (K); V₁, V₂ = initial and final volumes; P₁, P₂ = initial and final pressures.
Work in Isothermal Irreversible Process:
W = −Pext(V2 − V1)
-
Expansion: ΔV > 0 → W_expansion is positive (work done by system → negative sign)
-
Contraction: ΔV < 0 → W_contraction is positive
Work in Free Expansion-
When a gas expands into a vacuum (Pext = 0): W = 0
No work is done, regardless of whether the process is reversible or irreversible.
Key Points: Concept of Maximum Work
For maximum work, the external pressure must be infinitesimally smaller than the internal pressure of the gas (near-reversible conditions).
Wrev = Wmax
The maximum work is obtained only from a thermodynamically reversible change.
Key Points: Internal Energy (U)
Every system is associated with a definite amount of energy stored in it, called its internal energy (U). It is the sum of all forms of kinetic and potential energies of the particles in the system.
- Internal energy is a state function — its change depends only on initial and final states.
- It is an extensive property.
Internal energy changes when:
- Heat flows into or out of the system
- Work is done on or by the system
- Matter enters or leaves the system
ΔU = U2 − U1
Key Points: First Law of Thermodynamics
First Law: Energy of system + surroundings remains constant → ΔU = q + W
ΔU: change in internal energy, q: heat, W: work done on system
Sign convention:
- Work by system (−)
- on system (+)
- Heat absorbed (+)
- released (−)
ΔU > 0: energy enters system; ΔU < 0: energy leaves system
- Isothermal: ΔU = 0 → q = −W
- Adiabatic: q = 0 → ΔU = W
- Isochoric: W = 0 → ΔU = q
- Isobaric: ΔU = q + W
Key Points: Enthalpies of Physical Transformations
| Enthalpy | Meaning |
|---|---|
| Enthalpy of Fusion (ΔfusH) | Heat required to convert solid → liquid (1 mole) |
| Enthalpy of Vaporisation (ΔvapH) | Heat required to convert liquid → gas (at boiling point) |
| Enthalpy of Sublimation (ΔsubH) | Heat required to convert solid → gas directly |
| Enthalpy of Ionisation (ΔionH) | Energy required to remove an electron from a gaseous atom |
| Enthalpy of Atomisation (ΔatomH) | Energy required to form gaseous atoms from a substance |
| Enthalpy of Solution (ΔsolH) | Heat changes when a solute dissolves in a solvent |
Key Points: Thermochemistry
- Thermochemistry deals with heat energy changes during chemical reactions
- Enthalpy change (ΔH) = difference between products and reactants → ΔH = Hp − Hr
- Exothermic reactions: ΔH < 0, heat is released to the surroundings
- Endothermic reactions: ΔH > 0, heat is absorbed by the system
- Standard enthalpy (ΔH°) measured at 298 K and 1 bar pressure
- Enthalpy of formation (ΔfH°): formation of 1 mole; for elements = 0
- Enthalpy of combustion (ΔcH°): always negative (heat released)
- Bond enthalpy: energy required to break bonds in the gaseous state
- Reaction enthalpy using bond energy:
ΔrH° = ΣBE(reactants) − ΣBE(products) - Hess’s Law: total ΔH is the same for any path → ΔH = sum of individual steps
Key Points: Spontaneous (Irreversible) Process
- Spontaneous processes are those that occur naturally without any external force. They proceed in one direction and cannot be reversed unless an external influence is applied.
- Entropy is a measure of disorder or randomness in a system. Greater disorder means higher entropy.
- Entropy and spontaneity: In a spontaneous process, the entropy of the system tends to increase.
Key Points: Types of system
| Type of System | Exchange of Energy | Exchange of Matter | Example |
|---|---|---|---|
| Open System | Energy is exchanged with surroundings | Matter is exchanged with surroundings | Example: Open cup of hot coffee. It releases heat to surroundings and water vapour escapes into air. |
| Closed System | Energy is exchanged with surroundings | Matter is not exchanged with surroundings | Example: Hot coffee covered with saucer. It loses heat but water vapour does not escape. |
| Isolated System | No exchange of energy | No exchange of matter | Example: Insulated cup of coffee. Neither heat nor water vapour escapes to surroundings. |
Key Points: Nature of heat and work
- In mechanics, work is defined as force multiplied by displacement, given by the formula W = f × d.
- In thermodynamics, the work involved is pressure–volume work (PV work), which is done when a gas expands or contracts against an external opposing pressure.
- PV work is given by the expression W = −Pₑₓₜ ΔV, where ΔV is the change in volume.
- When a gas expands, it does work on the surroundings; when it is compressed, work is done on the system by the surroundings.
- Heat (Q) is a form of energy that is exchanged between the system and surroundings due to temperature difference.
- According to sign convention, +Q means heat absorbed by the system, −Q means heat released, +W means work done on the system, and −W means work done by the system; both heat and work are path functions.
Key Points: Expression for pressure-volume (PV) work
- Pressure–volume (PV) work is done when a gas expands or compresses against an external pressure in a cylinder fitted with a movable piston.
- The force exerted by the gas on the piston is equal to external pressure multiplied by area, given by
f = −Pₑₓₜ A. - Work done is equal to force multiplied by displacement, therefore
W = f × d. - Since change in volume is equal to area × displacement,
ΔV = A × d,
the expression for PV work becomes
W = −Pₑₓₜ ΔV = −Pₑₓₜ (V₂ − V₁). - During expansion (V₂ > V₁), work is done by the system on the surroundings and W is negative; during compression (V₂ < V₁), work is done on the system and W is positive.
- In free expansion (expansion in vacuum), external pressure is zero (Pₑₓₜ = 0), therefore
W = 0, and no work is done.
Important Questions [25]
- Define Adiabatic process.
- Define the extensive properties.
- Define Intensive property.
- Calculate the work done during the expansion of 2 moles of an ideal gas from 10 dm3 to 20 dm3 at 298 K in a vacuum.
- Write the sign convention of work done during expansion of gas.
- Three moles of an ideal gas are expanded isothermally from 15 dm3 to 20 dm3 at a constant external pressure of 1.2 bar. Calculate the amount of work in Joules.
- 2000 mmol of an ideal gas expanded isothermally and reversibly from 20 L to 30 L at 300 K, calculate the work done in the process (R = 8.314 JK–1 mol–1).
- One mole of an ideal gas is expanded isothermally and reversibly from 10 L to 15 L at 300 K. Calculate the work done in the process.
- Derive an expression for maximum work in isothermal reversible expansion of two moles of an ideal gas.
- Write one statement of first law of thermodyamics and its mathematical expression
- Calculate the internal energy at 298K for the formation of one mole of ammonia, if the enthalpy change at constant pressure is – 42.0 kJ mol-1. (Given: R = 8.314 J K-1 mol-1)
- Write the mathematical equation of the first law of thermodynamics for an isochoric process.
- Write mathematical equation of first law of thermodynamics for Adiabatic process
- Prove that ΔH=ΔU+ΔnRT. what is the condition under which ΔU=ΔH?
- Obtain the relationship between ΔH and ΔU for gas phase reactions.
- The enthalpy change for the chemical reaction HA2OA(s)⟶HA2OA(l) is called enthalpy of ______.
- Calculate the time required to deposit 2.4 g of Cu, when 2.03 A of current passed through CuSOA4, solution. (At. mass of Cu = 63.5 g mol−1)
- Calculate the standard enthalpy of formation of CH3OH(l) from the following data: [\ce{CH3OH_{(l)} + 3/2 O2_{(g)} -> CO2_{(g)} + 2H2O_{(l)}ΔH^° = - 726 kJ mol^{-1}}]
- Calculate the standard enthalpy of the reaction: SiO2(s) + 3C(graphite) → SiC(s) + 2CO(g) from the following reactions: Si(s) + O2(g) → SiO2(s),
- Define the Standard enthalpy of combustion
- Calculate the standard enthalpy of combustion of methane if the standard enthalpy of formation of methane, carbon dioxide and water are −74.8, −393.5 and −285.8 kJmol−1 respectively.
- Write the correct condition for spontaneity in terms of Gibbs energy.
- Answer the following in one or two sentences. State second law of thermodynamics in terms of entropy.
- For a certain reaction ΔH0 is −224 kJ and ΔS0 is −153 J K−1. At what temperature the change over from spontaneous to non-spontaneous will occur?
- Define entropy.
Concepts [12]
- Chemical Thermodynamics
- Terms Used in Thermodynamics
- Nature of Heat and Work
- Expression for Pressure-volume (PV) Work
- Concept of Maximum Work
- Internal Energy (U)
- First Law of Thermodynamics
- Enthalpy (H)
- Enthalpies of Physical Transformations
- Thermochemistry
- Spontaneous (Irreversible) Process
- Overview of Chemical Thermodynamics
