Internal Energy vs Enthalpy

Difference between internal energy and enthalpy is in the different modes of interception of energy (heat). Internal energy is the heat content of a system i.e. sum of all types of characteristic energies of a system whereas, enthalpy is the amount of heat either liberated or engaged in a system.

For a thermodynamic system, heat energy if studied under constant volume is called Internal energy, and the same heat energy if studied under constant pressure is called enthalpy of a system.

Difference between Internal energy and Enthalpy

Categories Internal Energy Enthalpy
Definition It is the sum of kinetic energy and potential energy. It is the amount of heat absorbed or released during a chemical reaction.
Symbolic representation It is represented by E or U. It is represented by H.
Principle Internal energy increases when systems absorb energy and decreases when systems release energy to the surrounding. Endothermic reactions have positive H and exothermic reactions have negative H
Application by principle For closed systems, the term internal energy is used. For open systems, the term enthalpy is used.
General Formula The formula of internal energy is U=q-W The formula of enthalpy is H=U+PV
Interpretation of formula According to the formula, change in internal energy is equal to heat transfer to the system minus work done. According to the formula, enthalpy is equal to the sum of internal energy and product of pressure-volume work.
Unit Its unit is Joule. Its unit is Joule/mole.
Condition It is a state of matter. It is an energy change between two states.
Type of function It is a state function. It is also a state function.
Property of matter It is an extensive property. It is also an extensive property.
Dependence Internal energy is a function of temperature. Enthalpy is a function of temperature and pressure.
Change At constant temperature U=0 At constant temperature, H=0 because U=0 and pressure-volume remain constant.
Measurement It cannot be measured directly. It can also not be measured directly.
Energy comparison The internal energy of the ideal gas is 40% less than enthalpy. Enthalpy of an ideal gas is 40% more than internal energy.
Conclusion Internal energy is the total energy in a system. It is an energy change between the system and the surroundings.
Example A glass of water has no apparent energy but it does have internal energy. H can be applied to refrigerators (freezing), boilers (boiling) etc.

Internal energy vs Enthalpy on operational basis

If q is the amount of heat absorbed by the system from surroundings:

Heat (q) (at constant volume) = Internal energy (U)

Heat (q) (at constant pressure) = Enthalpy (H)

Any of the terms in the above equations may either be positive or negative. The process can be exothermic, where heat (q) is negative and is released by the system into the surrounding. On the other hand, an endothermic process is the one in which heat (q) is positive, indicating that heat is taken by the system from the surroundings. If the system under consideration is neither exothermic nor endothermic, the system must be at equilibrium.

We cannot determine the absolute value of internal energy but we can determine the change in internal energy. This is because internal energy is the sum of various types of energies of a system that cannot be calculated.

Internal energy (U) = K.E(rotational)+ K.E(vibrational)+ K.E(translational)+ P.E(force of attraction)+ Binding energy

Similarly, the absolute value of enthalpy cannot be calculated but a change in enthalpy can be calculated.

Enthalpy (ΔH) = Final enthalpy (Hf) – Initial enthalpy (Hi)

Internal Energy

Internal energy is the sum of kinetic and potential energy of a system. Internal energy is the total heat content of atoms, molecules, electrons, and protons, in short everything present inside specific matter.

When heat is absorbed by a system, a part of absorbed energy (heat) may be used for doing work. A part of the total amount of energy within the system is associated with rearrangements of the atoms that occur in chemical reactions, the energy of interactions among atoms and molecules, and the energy associated with simply having a temperature. This stored amount of energy is called internal energy. It is represented by E or U.

When a system absorbs heat, it undergoes some modification, such as an increase in temperature, a change in physical state, or a chemical reaction taking place, depending upon what conditions the process occurs on.

For example
Internal energy

 

The amount of heat absorbed is used to increase the internal energy if no work is done by the system. This is only possible if a reaction is taking place in a closed vessel so that no expansion could take place.

Plotting this idea on a graph gives a curve showing linearity between internal energy and temperature.

Expansion and other works are not possible by the system if proper closure of system is obtained. Hence, all the heat absorbed converts to internal energy.

Obviously, this is only possible in ideal cases as such a tightly pack system is not available where the heat lost is exactly zero.

Most reactions take place in open vessels. It means some work is either done by the system or by the surroundings of the system.

According to the principle of conservation of energy, the amount of heat must adjust itself to provide a significant amount of work done. We already discussed work done in a closed system i.e Internal energy (U) but a thorough briefing on work done in an open system is also required, therefore, a new function, the enthalpy (H) is introduced which is related to heat flow in an open system.

Enthalpy

The amount of heat absorbed or released during a chemical reaction is exactly equal to enthalpy (H). Enthalpy is the sum of internal energy and product of pressure-volume work.

H = U + PV

As U, P and V are state functions, so enthalpy is a state function.

At constant pressure, energy supplied to a system as heat is equal to the enthalpy change.  Because of this relation, enthalpy is often called “heat of the reaction”. This relation can be proved by the following derivation.

Relationship between enthalpy change and heat transfer at constant pressure

H = U + PV

The changes in states of a system are represented as delta (d), as volume, pressure and internal energy are the changing factors, enthalpy also changes.

H = U + PV

H + dH = (U+dU) + PV + d(PV)

Simplifying,

H + dH = (U+dU) + (P+dP)(V+dV)

H + dH = U + dU + PV + PdV + VdP + dPdV

Since (dPdV) is a very small term ≈ 0

H + dH = U + PV + dU + PdV + VdP

As U + PV = H, the above equation becomes:

H + dH = H+dU + PdV + VdP

dH = dU + PdV + VdP

Now applying the condition of constant pressure where the change in pressure (dP) = 0

dH = dU + PdV ——- Eq(1)

From the first law of thermodynamics, we get

dU = dQ + PdV ——-Eq(2)

If a system is in mechanical equilibrium with its surrounding at pressure P and does expansion work then dW = -PdV

(Work done by the system is negative)

dU = dQ – PdV

Put this value in eq(1)

dH = dQ – PdV + PdV

dH = dQ – PdV + PdV

(dH)p = (dQ)p

This equation states that the change in enthalpy is equal to the energy supplied as heat at constant pressure.

Measurement of the enthalpy change

The change in enthalpy can be measured by the difference between final enthalpy (enthalpy of products) and initial enthalpy (enthalpy of reactants).

Enthalpy change = Final enthalpy – Initial enthalpy

∆H = Hf – Hi

where,

Hf = enthalpy of product

Hi = enthalpy of reactants

Specific enthalpy

Specific enthalpy is defined as enthalpy per unit mass of a substance.

Specific enthalpy (h) = Enthalpy (H) / mass (m)

It is measured in Joule/kg.

Effect of temperature on enthalpy

As temperature increases, the kinetic energy of particles in a system increases. This gives rise to internal energy and eventually, enthalpy (H) also increases.

Enthalpy of phase transitions

Enthalpy change of atomisation

It is the enthalpy change when 1 mole of gaseous atoms are formed from constituent elements. It is denoted by ∆Hatm.

For example

Li (s)  →  Li (g)               ∆Hatm = +161 KJ/mol

The enthalpy change of atomization of lithium is = +161 kJ/mol.

The value of enthalpy change is positive because the reaction is endothermic and work is done by surroundings on the system.

Enthalpy change of solution

It is the amount of heat absorbed or liberated when a substance is dissolved in a solvent to form an infinitely dilute solution. It is denoted by ∆Hsol.

Enthalpy change of solution may either be positive or negative.

MgCl2 (s) + aq → MgCl2 (aq)               ∆Hsol = -55 KJ/mol

NaCl (s) + aq   NaCl (aq)               ∆Hsol =+3.9 kJ/mol

Enthalpy change of hydration

It is the change in enthalpy when 1 mole of gaseous ions are dissolved in water to form an infinitely dilute solution. It is denoted by ∆Hhyd. It is always negative.

Cl(g) + H2O (aq)   Cl(aq)               ∆Hhyd = -364 kJ/mol

Enthalpy change of neutralization

It is the change in enthalpy when 1 mole of acid reacts with a base to form salt and water. It is denoted by ∆Hneut.

HCl + NaOH   NaCl + H2O               ∆Hneut  = -57.9 kJ/mol

Enthalpy change of vaporization

It is also called heat of evaporation. The amount of heat required to convert 1 mole of a liquid into a gas is called enthalpy change of vaporization. It is denoted by ∆Hvap.

The heat of vaporization of water is 40.8kJ/mol.

H2O (liq)  →  H2O (gas)               ∆Hvap  =  -40.8 kJ/mol

Enthalpy of hydrogenation

It is the enthalpy change when 1 mole of an unsaturated compound reacts with hydrogen to form a saturated compound. It can be denoted by ∆Hhydrogenation.

1-butene + H2  →  1-butane               ∆Hhydrogenation= -30.3 kcalmol-1

Enthalpy of denaturation

It is defined as the enthalpy change required to denature 1 mol of a compound. It is denoted by ∆Hden.

Enthalpy of sublimation

It is defined as the enthalpy change required to convert 1 mole of solid into its gaseous state. It is denoted by ∆Hsub.

I2 (s)   →   I2 (g)                     ∆Hsub= 106 kJmol-1

Lattice enthalpy

It is defined as enthalpy change required when 1 mol of an ionic compound is converted into its gaseous ions to an infinite distance apart. It is denoted by ∆Hlatt.

NaCl (s)   →   Na+(g) + Cl(g)               ∆Hlatt  =  769 kJmol-1

Enthalpy of mixing

It is defined as enthalpy change upon mixing two chemical substances.

For ideal gases, the enthalpy of mixing is zero because there are no interactions between the particles.

For ideal solutions, the solvent-solvent and solute-solute interactions are stronger than solute-solvent interactions, so the net enthalpy is zero.

Key takeaways

Internal energy vs enthalpy

Concepts Berg

What is internal energy?

Internal energy is the sum of all kinds of energies in a system. It is the total energy contained in a system. It is due to the translational, vibrational, and rotational motion of atoms in a molecule. It is also due to interactions between the molecules.

It is represented by either E or U.

What is the relation between enthalpy and internal energy?

Internal energy is the total energy contained in a system where enthalpy is the total heat content of a system.

Enthalpy is equal to the sum of internal energy and product of pressure-volume work.

H = U + PV

The first law of thermodynamics states that a change in internal energy is equal to the heat added to a system minus work done by the system.

U = Q – W

Both are state functions and both are extensive properties.

What is the difference between energy and enthalpy?

Energy is a state of matter whereas Enthalpy is an energy change between two states of a particular system.

Energy is measured in Joules whereas enthalpy is measured in Joule/mol.

Energy is a function of temperature whereas enthalpy is a function of temperature and pressure.

Should I use enthalpy or internal energy?

When heat is added to a system at constant volume, we use the term internal energy because no work is done and it is a closed system.

When heat is added to a system at constant pressure then we use the term enthalpy because work is done and it is an open system.

If q is the amount of heat absorbed by the system from surroundings,

Heat (q) (at constant volume) = Internal energy (E)

Heat (q) (at constant pressure) = Enthalpy (H)

What is the internal energy formula?

The first law of thermodynamics states that any change in internal energy is equal to the heat added to a system minus work done by the system.

dU = Q – dW

where dU = change in internal energy

Q = heat added into a system

dW =  work done by the system

Is enthalpy just energy?

Enthalpy is the sum of internal energy and product of pressure-volume work. Energy is a state of matter where enthalpy is an energy change between two states. So, enthalpy is not just energy.

What does it mean when enthalpy is zero?

Zero enthalpy means reactants and products are identical. As enthalpy is a state function, if initial and final enthalpies are equal then the change in enthalpy is zero. It also means that there exists either no reaction or complete equilibrium.

Why is enthalpy used instead of internal energy?

If a reaction occurs at constant volume, then added heat is equal to a change in internal energy.

If a chemical reaction occurs at constant pressure, then enthalpy is used to measure the heat of the reaction instead of internal energy.

Can enthalpy be greater than internal energy?

For an open system, the term enthalpy is used to calculate energy and it is always greater than internal energy.

The enthalpy of an ideal gas is 40% greater than its internal energy.

Why do we need enthalpy?

Enthalpy is used to calculate the heat of the reaction at constant pressure.

To know about the nature of the reaction whether it is exothermic or endothermic the term enthalpy is used.

  • When enthalpy (H) is positive,  the reaction is endothermic.
  • When enthalpy (H) is negative, the reaction is exothermic.

Why is enthalpy greater than internal energy?

Internal energy is a heat of reaction at a constant volume where enthalpy is a heat of reaction plus pressure-volume work at constant pressure. This additional factor of pressure-volume work makes the enthalpy of an ideal gas 40% greater than its internal energy.

What is the internal energy of the gas formula?

The internal energy of a gas is calculated by a formula

Internal energy (U) = 3/2 NKT

Where N is the number of atoms in the gas.

In a constant volume process, the internal energy change is equal to?

At constant volume, the change in internal energy is equal to the amount of heat absorbed in a system.

From the 1st law of thermodynamics,

dq = dU + dW

(dq)v = (du)v

What is the difference between internal energy and entropy?

Internal energy is the measure of the total energy contained in a system while entropy is the measure of the degree of randomness in a system.

The unit of internal energy is Joule whereas the unit of entropy is the Joule/Kelvin mole.

What is the enthalpy of products or reactants?

Enthalpy of product is the total heat content per mole of product and enthalpy of reactant is the total heat content per mole of reactant.

Enthalpy of reaction is the difference between the enthalpy of products and the enthalpy of reactants.

Can enthalpy be negative?

We cannot measure the absolute value of enthalpy. Only the change in enthalpy can be measured. So, the change in enthalpy may be positive or negative. For exothermic reactions, the change in enthalpy is negative whereas for endothermic reactions, the change in enthalpy is positive.

Can we define enthalpy for solids and liquids?

We cannot define the enthalpy of solids and liquids. We can only define the enthalpy change for solids and liquids.

Is the internal energy of a solid and gas the same, provided the temperature and number of moles are the same?

Internal energies of the solid and the gas are not same. When the temperature increases, kinetic energy increases and resulting is an increase in internal energy. However, the increase in internal energy in case of gases is more than solids because of the degree of freedom.

Why is internal energy considered to be an extensive property?

Internal energy depends on the amount of substance, that’s why it is an extensive property.

What happens to the internal energy if work is done by the system?

If heat is released from the system to surroundings and work is done by the system then internal energy decreases.

What is the significance of enthalpy?

Enthalpy is used to calculate the heat of the reaction at constant pressure.

It tells us whether the reaction is endothermic or exothermic.

It is the measure of the amount of heat absorbed or released during a chemical reaction.

What is the difference between heat and energy?

Heat is a transfer of energy from a body of high temperature to a body of lower temperature.

Energy is the ability of a body to do work.

What is the difference between heat and enthalpy?

Heat is a transfer of energy due to temperature differences. Enthalpy is the change in the amount of heat at constant pressure.

Why is internal energy directly proportional to temperature since internal energy increases during a phase change but the temperature does not?

During a phase change, energy is absorbed or released. For example, change in phase from solid to liquid and from liquid to gas requires energy so internal energy increases.

Temperature is directly proportional to the kinetic energy of particles. During a phase change, kinetic energy does not increase so does the temperature.

What is the reason for using the Cp value to find change in enthalpy for all non-flow processes. Why can’t we use Cv?

In non-flow processes, constant pressure exists. So, we use Cp rather than Cv.

What is the specific enthalpy?

Specific enthalpy is defined as enthalpy per unit mass of a substance. It is measured in Joule/kg.

Specific enthalpy (h) = Enthalpy (H) / mass (m)

How will the internal energy change during the boiling process?

In the boiling process, energy is required to convert liquid into the gas phase. As water molecules gain energy, they speed up and their internal energy changes.

In the adiabatic process what happens to internal energy when a gas expands adiabatically?

In adiabatic expansion, no heat enters or leaves the system, and work is done by the gas. So, internal energy decreases and the temperature of the system falls.

In an isothermal process, the change in internal energy is zero. Why?

In isothermal process, the temperature remains constant. As internal energy is directly proportional to temperature, so if the temperature change is zero, the change in internal energy is also zero.

Why is the ionization enthalpy of Tl greater than that of In?

The nuclear charge in the case of TI is greater than that of In. This means that the shielding effect of TI is greater than In. So, removal of the outermost electron from TI is difficult. That’s why, it has more ionization enthalpy.

What’s the difference between heat and light energy?

Heat and light both are forms of energy. Heat is defined as energy transfer due to temperature differences. Light is a form of electromagnetic radiation.

Light energy can be converted into heat energy and vice versa.

What is flow energy?

The energy of flowing fluid is called flow energy. The flowing fluid can do work on the piston placed in its path.

What is the difference between heat and thermal energy?

Heat is the energy transfer due to temperature differences while the energy which comes from the temperature of a heated substance is called thermal energy.

Heat is an energy in transit, while thermal energy is not in transit.

What are the differences and similarities between evaporation and boiling?

Both evaporation and boiling involve the change of liquid state into gas.

Evaporation occurs at all temperatures but boiling only occurs at the boiling point of a liquid.

Evaporation is a slow process while boiling is a fast process.

Why are experimental lattice enthalpy values greater than theoretical lattice enthalpy values?

The experimental value of lattice enthalpy is greater because, in ionic bonds, the covalent character is also present. So a larger amount of energy is required to break the lattice than observed in theoretical values.

What is the difference between heat and kinetic energy?

Heat is a form of kinetic energy. When we heat a substance, its temperature increases so does it’s kinetic energy.

All heat energy is kinetic energy but all kinetic energy is not the heat energy.

What is the difference between endothermic and exothermic reactions if both require activation energy?

Both exothermic and endothermic reactions require activation energy to take place.

In an endothermic reaction, the energy of the products is greater than the energy of reactants. So it requires more activation energy.

In an exothermic reaction, the energy of reactants is greater than the energy of the products. So it requires less activation energy.

Is the ice melting considered endothermic or exothermic, Why?

Melting of ice is an endothermic reaction as the ice absorbs energy from surrounding to change its state from solid to liquid.

What is the temperature inside the combustion chamber of an engine?

The temperature inside the combustion chamber of an engine can reach 4500o F.

What is the difference between isentropic and polytropic processes in thermodynamics?

Isentropic processes are adiabatic and reversible. They are ideal processes. No heat transfer and loss takes place in these processes.

The processes other than isentropic processes are called polytropic processes. They are real processes and obey the relation

PVn = C

where P is pressure, V is volume, and the ‘n’ and ‘C’ are constants.

What is the relation between temperature-pressure for liquid?

The relationship between temperature and pressure of the liquid is given by the Clausius-Clapeyron equation,

ln (P2 – P1) = H/R (1/T1 – 1/T2)

where

H = change in enthalpy

R = general gas constant

P, T = pressure and temperature

If internal combustion engines work due to the expansion of gases in the cylinder why are they classified as heat engines?

Internal combustion engines do work on the principle of expansion of gases but this doesn’t mean that this phenomenon runs on its own. Sometimes, there are linkages between driving principles. The expansion phenomenon runs with the help of the thermal expansion principle of fluids. So, the main driving principle behind internal combustion engines is ‘heat’ not ‘expansion’. That’s why, they are called heat engines.

What is the gamma ratio of specific heats Cp, Cv of water?

The ratio of specific heat capacity at constant pressure to the specific heat capacity at constant volume is called gamma.

The value of gamma for water is 9.807.

What is the difference between thermodynamics and heat transfer?

Thermodynamics deals with the relationship between energy and work. Where heat describes the transport of energy.

Does global warming increase entropy on Earth or vice versa?

Entropy is a function of temperature. When temperature increases, it may lead to an increase in entropy. An increase in entropy means more energy is spread out which increases global warming.

When do we use Cp and Cv in thermodynamic equations?

Cp is used when there is a specific heat capacity at constant pressure. Similarly, CV is used when there is a specific heat capacity at a constant volume.

Under Cv, the volume change is zero where under Cp the change in pressure is zero.

Are fire and electricity the same thing?

Electricity is due to the flow of free electrons. Fire takes place when a substance reacts with oxygen. So, fire and electricity are different.

What happens to the entropy of a cube of ice as it is melted?

Entropy is the measure of randomness in a system. The greater the randomness in a system, the greater will be its entropy. As ice melts, solid is converted into liquid. The molecules of a liquid are in a more disordered state so entropy increases.

What is the concept of adiabatic demagnetization?

It is a process in which a magnetic field is removed from a certain material so that it gets lower temperature.

What is the relation between density and specific heat?

Density is defined as mass per unit volume. Specific heat is the amount of heat required to raise the temperature of 1 gram of substance through 1 Kelvin.

There is no correlation between these two terms.

How much heat is generated by LED light bulbs?

A typical light bulb generates 15% of visible light and 85% heat.

What is Cp – Cv = R ?

This equation relates general gas constant with heat capacity at constant pressure and heat capacity at constant volume.

Laplace uses the ratio of Cp and Cv which is called to calculate the ‘speed of sound’.

How are entropy and temperature related?

Entropy and temperature are related to each other. When temperature increases the kinetic energy of particles increases which increases their randomness so entropy also increases.

References

https://chem.libretexts.org/internal-energy/

https://byjus.com/chemistry/internal-energy/

Schaum’s Outlines-College Chemistry (9th edition) by Jerome L. Rosenberg, Ph.D. Lawrence M. Epstein, Ph.D. Peter J.Krieger, Ed.D.