Internal Energy and Enthalpy

Thermodynamics me internal energy (U) aur enthalpy (H) fundamental properties hain jo energy transfer, work, heat, aur thermodynamic processes ko describe karte hain. Ye dono concepts engineering, chemistry, physics, aur daily life applications me crucial hain, jaise heat engines, refrigeration, chemical reactions, aur material science.

1. Introduction

Thermodynamics energy ke transfer aur transformation ka study hai. Energy ka analysis karne ke liye state functions ki zarurat hoti hai.

Internal Energy (U): System ke particles ki microscopic energy, jo kinetic aur potential energy ka sum hoti hai.
Enthalpy (H): System ki total heat content at constant pressure, useful for chemical and engineering processes.

Ye concepts First Law of Thermodynamics aur heat-work relationships ke liye base provide karte hain.

2. Internal Energy (U)

2.1 Definition

Internal energy (U):

The total microscopic energy possessed by a system due to motion and interaction of its molecules.

Components:

Kinetic energy (KE): Translational, rotational, vibrational motion
Potential energy (PE): Intermolecular forces, chemical bonds

Mathematically: U=KE+PEU = KE + PEU=KE+PE

Key points:

State function → depends only on current state, not path
Absolute value unknown → only changes (ΔU) measurable

2.2 Internal Energy in Ideal Gases

For ideal gases:

No intermolecular forces → PE negligible
Internal energy depends only on temperature

U=f2nRTU = \frac{f}{2} n R TU=2fnRT

Where:

fff = degrees of freedom (monoatomic = 3, diatomic = 5, polyatomic = 6)
nnn = moles
RRR = universal gas constant
TTT = temperature (K)

Change in internal energy: ΔU=nCvΔT\Delta U = n C_v \Delta TΔU=nCvΔT

CvC_vCv = molar specific heat at constant volume

2.3 Internal Energy and First Law of Thermodynamics

First law: ΔU=Q−W\Delta U = Q – WΔU=Q−W

ΔU\Delta UΔU → internal energy change
QQQ → heat added to system
WWW → work done by system

Examples:

Isochoric process (V constant): W = 0 → ΔU = Q
Adiabatic process (Q = 0): ΔU = -W

2.4 Measurement of Internal Energy

Direct measurement difficult
Only changes (ΔU) measured via heat and work interactions
Example: Heating gas in piston → ΔU = Q – W

3. Enthalpy (H)

3.1 Definition

Enthalpy (H):

The total heat content of a system at constant pressure, defined as:

H=U+PVH = U + PVH=U+PV

Where:

UUU = internal energy
PPP = pressure
VVV = volume
State function → depends only on current state

3.2 Physical Significance

Enthalpy represents energy needed for system to create space for itself (PV work) plus internal energy.
Useful for constant pressure processes like chemical reactions, phase changes, and heat engines.

3.3 Change in Enthalpy

ΔH=ΔU+Δ(PV)\Delta H = \Delta U + \Delta(PV)ΔH=ΔU+Δ(PV)

For ideal gas (PV = nRT):

ΔH=ΔU+nRΔT\Delta H = \Delta U + n R \Delta TΔH=ΔU+nRΔT

For constant pressure:

ΔH=QP\Delta H = Q_PΔH=QP

Where QPQ_PQP = heat added at constant pressure

3.4 Relation Between Enthalpy and Specific Heat

Molar heat capacities:

Cp=(∂H∂T)PC_p = \left(\frac{\partial H}{\partial T}\right)_PCp=(∂T∂H)P Cv=(∂U∂T)VC_v = \left(\frac{\partial U}{\partial T}\right)_VCv=(∂T∂U)V

For ideal gas: Cp−Cv=RC_p – C_v = RCp−Cv=R

4. Internal Energy vs Enthalpy

Feature	Internal Energy (U)	Enthalpy (H)
Definition	Total microscopic energy	Total heat content (U+PV)
State function	Yes	Yes
Useful for	Isochoric/adiabatic processes	Constant pressure processes
Symbol	U	H
Units	Joule (J)	Joule (J)

5. Application in Thermodynamic Processes

5.1 Isochoric Process (V constant)

W = 0 → ΔU = Q
ΔH = ΔU + PΔV → ΔH = ΔU (since ΔV = 0)

5.2 Isobaric Process (P constant)

ΔH = Q_P → Heat added equals change in enthalpy
Work done: W = PΔV

5.3 Adiabatic Process (Q = 0)

ΔU = -W
ΔH = ΔU + Δ(PV)

5.4 Isothermal Process (ΔT = 0)

ΔU = 0
ΔH = Δ(PV) → work done related to PV changes

6. Enthalpy of Phase Changes

Latent heat of fusion (melting):

ΔHfus=Qfusion=mLf\Delta H_{fus} = Q_{fusion} = m L_fΔHfus=Qfusion=mLf

Latent heat of vaporization (boiling):

ΔHvap=Qvaporization=mLv\Delta H_{vap} = Q_{vaporization} = m L_vΔHvap=Qvaporization=mLv

Temperature constant during phase change
Heat absorbed → changes enthalpy

7. Enthalpy of Chemical Reactions

Heat released/absorbed in chemical reactions at constant pressure = ΔH

Exothermic reaction: ΔH < 0 → heat released
Endothermic reaction: ΔH > 0 → heat absorbed

Example: Combustion of methane:

CH4+2O2→CO2+2H2O+QCH_4 + 2O_2 \rightarrow CO_2 + 2H_2O + QCH4+2O2→CO2+2H2O+Q

ΔH = -890 kJ/mol → exothermic

8. Graphical Representation

P-V Diagram: Area under curve = work
T-S Diagram: Area under curve = heat transfer
Enthalpy vs Temperature: Slope = C_p, plateau = phase change

9. Real-World Applications

Heat Engines: Use ΔU and ΔH to calculate work and efficiency
Refrigeration: Enthalpy used to design compressors and evaporators
Chemical Engineering: Determine heat requirements of reactions
Meteorology: Enthalpy used in calculating latent heat in atmospheric processes
Power Plants: Boilers, turbines, and condensers use U and H relationships

10. Experimental Measurement

Calorimetry: ΔH measured via calorimeters
Bomb Calorimeter: Measures ΔU for combustion reactions
Differential Scanning Calorimeter (DSC): Measures ΔH and specific heat

11. Summary Table

Property	Symbol	Definition/Formula	Unit
Internal Energy	U	Microscopic energy KE+PE	Joule (J)
Enthalpy	H	H = U + PV	Joule (J)
ΔU (ideal gas)	–	ΔU = nC_vΔT	Joule (J)
ΔH (ideal gas)	–	ΔH = nC_pΔT	Joule (J)
Heat at constant P	Q_P	Q_P = ΔH	Joule (J)
Heat at constant V	Q_V	Q_V = ΔU	Joule (J)