Question:

Which amongst the following options is the correct relation between change in enthalpy and change in internal energy

Updated On: Dec 6, 2025

\(ΔH = ΔU + Δn_gRT\)
\(ΔH - ΔU = - ΔnRT\)
\(ΔH + ΔU = ΔnR\)
\(ΔH = ΔU - Δn_gRT\)

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The Correct Option is A

Approach Solution - 1

In thermodynamics, the enthalpy change (\(ΔH\)) of a system is related to the change in internal energy (\(ΔU\)), pressure (\(P\)), volume (\(V\)), and temperature (\(T\)). The formal relationship is given by the equation:

\(ΔH = ΔU + PΔV\)

For reactions involving gases, the volume change can be expressed as \(ΔV = Δn_gRT\), where \(Δn_g\) is the change in the number of moles of gas, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin. Substituting this into the enthalpy equation gives:

\(ΔH = ΔU + Δn_gRT\)

This equation shows that the change in enthalpy is equal to the change in internal energy plus the work done by the system due to gas expansion or compression, represented by \(Δn_gRT\). The correct option is therefore:

\(ΔH = ΔU + Δn_gRT\)

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Approach Solution -2

The key relationship is:
ΔH = ΔU + PΔV,
where PΔV is the work done due to volume change.

For gases, PΔV = Δn_g RT (Δn_g is the change in moles of gas, R is the gas constant, T is temperature). So,
ΔH = ΔU + Δn_g RT.

Now, let’s check the options:

- Option 1: ΔH = ΔU + Δn_g RT (Matches the formula, so it’s correct).

- Option 2: ΔH = ΔU – Δn_g RT (Incorrect, doesn’t align with the general formula).

- Option 3: ΔH = ΔU – nR (Incorrect, missing Δn_g and doesn’t fit the relationship).

- Option 4: ΔH = –ΔU – Δn_g RT (Incorrect, contradicts the additive relationship).

Thus, the correct answer is Option 1: ΔH = ΔU + Δn_g RT.

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Concepts Used:

Thermodynamics

Thermodynamics in physics is a branch that deals with heat, work and temperature, and their relation to energy, radiation and physical properties of matter.

Important Terms

System

A thermodynamic system is a specific portion of matter with a definite boundary on which our attention is focused. The system boundary may be real or imaginary, fixed or deformable.

There are three types of systems:

Isolated System – An isolated system cannot exchange both energy and mass with its surroundings. The universe is considered an isolated system.
Closed System – Across the boundary of the closed system, the transfer of energy takes place but the transfer of mass doesn’t take place. Refrigerators and compression of gas in the piston-cylinder assembly are examples of closed systems.
Open System – In an open system, the mass and energy both may be transferred between the system and surroundings. A steam turbine is an example of an open system.

Thermodynamic Process

A system undergoes a thermodynamic process when there is some energetic change within the system that is associated with changes in pressure, volume and internal energy.

There are four types of thermodynamic process that have their unique properties, and they are:

Adiabatic Process – A process in which no heat transfer takes place.
Isochoric Process – A thermodynamic process taking place at constant volume is known as the isochoric process.
Isobaric Process – A process in which no change in pressure occurs.
Isothermal Process – A process in which no change in temperature occurs.

Laws of Thermodynamics

Zeroth Law of Thermodynamics

The Zeroth law of thermodynamics states that if two bodies are individually in equilibrium with a separate third body, then the first two bodies are also in thermal equilibrium with each other.

First Law of Thermodynamics

The First law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing three kinds of transfer of energy, as heat, as thermodynamic work, and as energy associated with matter transfer, and relating them to a function of a body's state, called internal energy.

Second Law of Thermodynamics

The Second law of thermodynamics is a physical law of thermodynamics about heat and loss in its conversion.

Third Law of Thermodynamics

Third law of thermodynamics states, regarding the properties of closed systems in thermodynamic equilibrium: The entropy of a system approaches a constant value when its temperature approaches absolute zero.