THERMODYNAMICS : 1 ( System, work done and internal energy
4.1 Thermodynamic System
Thermodynamics is the branch of physics that deals with heat, work, temperature, and their relation to energy and the properties of matter. Understanding thermodynamic systems is fundamental to analyzing energy transformations.
Definition of Thermodynamic System
Thermodynamic System:
"A thermodynamic system is a definite quantity of matter or a region of space chosen for study, separated from its surroundings by a boundary (real or imaginary)."
The system contains:
- A fixed quantity of matter (closed system) OR a fixed region of space (open system)
- Properties like pressure (P), volume (V), temperature (T), internal energy (U)
- Energy in forms of heat and work
Key Components
| Component | Description |
|---|---|
| System | The part of the universe chosen for thermodynamic analysis (e.g., gas in a cylinder, engine, refrigerator) |
| Surroundings | Everything outside the system that can interact with it (rest of the universe) |
| Boundary | Real or imaginary surface separating system from surroundings; can be rigid/movable, permeable/impermeable |
| Universe | System + Surroundings (the totality of system and surroundings) |
Types of Thermodynamic Systems
1. Open System (Control Volume)
Definition: A system that can exchange both matter and energy with surroundings.
Boundary: Permeable to matter and energy
Examples:
- Boiling water in an open pot (steam escapes, heat enters)
- Car engine (fuel enters, exhaust exits, heat released)
- Human body (food in, waste out, heat exchange)
- Open beaker with chemical reaction
2. Closed System (Control Mass)
Definition: A system that can exchange energy (heat, work) but NOT matter with surroundings.
Boundary: Impermeable to matter but allows energy transfer
Examples:
- Gas in a sealed cylinder with movable piston (can do work, exchange heat)
- Refrigerant in a refrigeration cycle
- Water in a pressure cooker (sealed, no mass escapes)
- Gas in a balloon (approximately closed)
3. Isolated System
Definition: A system that exchanges neither matter nor energy with surroundings.
Boundary: Impermeable to both matter and energy
Examples:
- Ideal thermos flask (perfectly insulated, sealed)
- The entire universe (by definition, nothing outside it)
- Coffee in a perfectly insulated container (theoretical)
Note: True isolated systems are theoretical; real systems always have some energy exchange.
Thermodynamic Properties
State Variables: Properties that define the state of a system
| Property | Symbol | Description |
|---|---|---|
| Pressure | P | Force per unit area exerted by gas molecules |
| Volume | V | Space occupied by the system |
| Temperature | T | Average kinetic energy of molecules |
| Internal Energy | U | Total energy of molecules (kinetic + potential) |
| Entropy | S | Measure of disorder or randomness |
| Enthalpy | H | H = U + PV (heat content at constant pressure) |
Thermodynamic Equilibrium
Thermodynamic Equilibrium:
A system is in thermodynamic equilibrium when its macroscopic properties (P, V, T) remain constant over time and there are no net flows of energy or matter within the system.
Three types of equilibrium must be satisfied:
1. Thermal Equilibrium:
- Temperature uniform throughout system
- No heat flow within system
- Example: Hot coffee left in room eventually reaches room temperature
2. Mechanical Equilibrium:
- Pressure uniform throughout (for fluids)
- No unbalanced forces
- No bulk motion or acceleration
- Example: Gas in a cylinder with piston at rest
3. Chemical Equilibrium:
- No net chemical reactions occurring
- Composition remains constant
- Example: Reversible reaction at equilibrium (forward rate = reverse rate)
Thermodynamic State and State Functions
State vs Path Functions:
State Functions (Point Functions):
- Depend ONLY on current state, NOT on path taken
- Examples: P, V, T, U (internal energy), H (enthalpy), S (entropy)
- Change is independent of process: ΔU = Ufinal - Uinitial
- Analogy: Altitude on a mountain (doesn't matter which trail you took)
Path Functions (Process Functions):
- Depend on the PATH or PROCESS taken
- Examples: Q (heat), W (work)
- Amount depends on how the change occurred
- Analogy: Distance traveled on mountain (depends on which trail)
Important: While Q and W are path-dependent, their difference (Q - W) equals ΔU, which is path-independent. This is the essence of the First Law of Thermodynamics.
Applications and Importance
- Engineering: Design of engines, refrigerators, power plants, turbines
- Chemistry: Understanding chemical reactions, equilibria, reaction spontaneity
- Biology: Metabolism, energy transfer in living organisms
- Meteorology: Weather patterns, atmospheric thermodynamics
- Astrophysics: Star formation, stellar evolution, black holes
4.2 Work Done By and On the System
In thermodynamics, work is energy transferred when a system changes its volume against external pressure. Understanding work is crucial for energy analysis of thermodynamic processes.
Sign Convention for Work
Sign Convention (Most Common):
- Work done BY the system (expansion): W > 0 (POSITIVE)
- Work done ON the system (compression): W < 0 (NEGATIVE)
Note: Some textbooks use opposite convention. Always check your textbook's convention. NEB typically uses the above convention.
Calculation of Work Done During Volume Change
Consider a gas in a cylinder with movable piston:
Force exerted by gas on piston: F = P × A
where P = pressure, A = cross-sectional area of piston
Work done when piston moves distance dx:
dW = F × dx = P × A × dx
But A × dx = dV (change in volume):
dW = P dV
Total work for volume change from V₁ to V₂:
W = ∫ P dV
For finite volume change from V₁ to V₂:
W = ∫V₁V₂ P dV
For constant pressure (isobaric process):
W = P(V₂ - V₁) = PΔV
P-V Diagram (Indicator Diagram)
A P-V diagram plots pressure (P) on the y-axis versus volume (V) on the x-axis. It's a powerful tool for visualizing thermodynamic processes and calculating work.
Key Principle: Work = Area Under P-V Curve
The work done by a gas during a process equals the area under the P-V curve for that process.
- Expansion (V₂ > V₁): Area is positive → W > 0 (work done BY system)
- Compression (V₂ < V₁): Area is negative → W < 0 (work done ON system)
- Cyclic Process: Net work = Area enclosed by the cycle
- Clockwise cycle → W > 0 (net work output, heat engine)
- Counterclockwise cycle → W < 0 (net work input, refrigerator/heat pump)
Work for Different Processes
| Process | Condition | Work Formula |
|---|---|---|
| Isobaric (Constant P) | P = constant | W = P(V₂ - V₁) = PΔV |
| Isothermal (Constant T) | T = constant, PV = constant | W = nRT ln(V₂/V₁) = P₁V₁ ln(V₂/V₁) |
| Isochoric (Constant V) | V = constant, ΔV = 0 | W = 0 (no volume change) |
| Adiabatic (No heat exchange) | Q = 0, PVγ = constant | W = (P₁V₁ - P₂V₂)/(γ - 1) = nR(T₁ - T₂)/(γ - 1) |
Important Points for NEB Exams:
- Sign convention: Expansion W > 0, Compression W < 0 (most common)
- Work is a path function (depends on process, not just initial and final states)
- Work = ∫ P dV = Area under P-V curve
- For constant pressure: W = PΔV (simplest formula)
- For constant volume: W = 0 (no work if volume doesn't change)
- Different paths between same initial and final states give different work values
- In cyclic processes, net work = area enclosed by cycle on P-V diagram
4.3 Latent Heat and Internal Energy
Understanding latent heat and internal energy is fundamental to thermodynamics. These concepts explain how energy is stored and transferred in matter.
Latent Heat
Latent Heat Definition:
"Latent heat is the amount of heat energy absorbed or released by a substance during a phase change (change of state) at constant temperature and pressure."
During phase transitions (solid ↔ liquid ↔ gas), temperature remains constant while heat is added or removed. This energy changes the intermolecular bonds rather than kinetic energy.
Q = mL
Where:
Q = Heat absorbed or released (J)
m = Mass of substance (kg)
L = Latent heat (J/kg or J/mol)
Types of Latent Heat
| Type | Phase Change | Description | Example for Water |
|---|---|---|---|
| Latent Heat of Fusion (Lf) | Solid ↔ Liquid | Heat needed to melt solid or released when liquid freezes | Lf = 334 kJ/kg (ice to water at 0°C) |
| Latent Heat of Vaporization (Lv) | Liquid ↔ Gas | Heat needed to boil liquid or released when vapor condenses | Lv = 2260 kJ/kg (water to steam at 100°C) |
| Latent Heat of Sublimation (Ls) | Solid ↔ Gas | Heat needed for solid to directly become gas | Dry ice (CO₂) sublimates at -78°C |
Why Does Temperature Remain Constant During Phase Change?
During melting, boiling, or sublimation:
- Energy is used to break intermolecular bonds, not to increase kinetic energy
- Breaking bonds requires energy (endothermic process)
- Temperature (measure of average KE) stays constant
- Molecular arrangement changes: ordered (solid) → less ordered (liquid) → disordered (gas)
Example: Ice at 0°C and water at 0°C have same temperature but different energy states. The water has more internal energy because bonds were broken during melting.
Internal Energy (U)
Internal Energy Definition:
"Internal energy is the total energy contained within a system, including the kinetic energy of molecular motion and the potential energy of intermolecular forces."
U = KE + PE
Where:
KE = Kinetic energy of molecules (translational, rotational, vibrational)
PE = Potential energy due to intermolecular forces
For ideal gas (no intermolecular forces, PE ≈ 0):
U = nCvT
Where:
n = number of moles
Cv = molar specific heat at constant volume
T = absolute temperature (K)
Types of Molecular Energy
| Energy Type | Description | Dependence |
|---|---|---|
| Translational KE | Energy due to linear motion of molecules | Present in all gases, liquids (some), solids (vibration) |
| Rotational KE | Energy due to rotation of molecules | Present in polyatomic molecules |
| Vibrational KE | Energy due to vibration of atoms within molecules | Present in solids and molecules at high T |
| Potential Energy | Energy due to intermolecular attractions/repulsions | Significant in liquids and solids, negligible in ideal gases |
Properties of Internal Energy
Key Properties:
1. State Function:
- Internal energy depends only on current state (P, V, T), not on path
- ΔU = Ufinal - Uinitial is path-independent
2. Temperature Dependence:
- For ideal gases: U ∝ T (directly proportional to temperature)
- Higher temperature → more molecular kinetic energy → higher U
3. Cannot Be Measured Absolutely:
- We can only measure changes in internal energy (ΔU)
- Absolute value of U is unknown (requires quantum mechanics)
4. Extensive Property:
- Depends on amount of substance
- Doubling mass doubles internal energy
Change in Internal Energy
Internal energy can change by two mechanisms:
1. Heat Transfer (Q):
- Energy transferred due to temperature difference
- Heat INTO system → ΔU increases (Q > 0)
- Heat OUT OF system → ΔU decreases (Q < 0)
2. Work (W):
- Energy transferred due to mechanical means (volume change, stirring, etc.)
- Work done ON system → ΔU increases (W < 0 in our convention, -W > 0)
- Work done BY system → ΔU decreases (W > 0 in our convention, -W < 0)
First Law of Thermodynamics combines both:
ΔU = Q - W
(We'll explore this in detail in section 4.4)
For Ideal Gas
U = nCvT
Change in internal energy:
ΔU = nCvΔT
For monatomic gas: Cv = (3/2)R, so U = (3/2)nRT
For diatomic gas: Cv = (5/2)R, so U = (5/2)nRT
Important: For ideal gas, ΔU depends only on temperature change, regardless of process!
Important for NEB Exams:
- Latent heat formula: Q = mL (no temperature change during phase transition)
- Lf (fusion) for ice to water: 334 kJ/kg at 0°C
- Lv (vaporization) for water to steam: 2260 kJ/kg at 100°C
- Internal energy U is a state function (path-independent)
- For ideal gas: U = nCvT, so ΔU = nCvΔT
- ΔU depends only on temperature change for ideal gas, not on P or V individually
- During isothermal process (T constant): ΔU = 0 for ideal gas