CHEP 121 Lecture Notes on the First Law of Thermodynamics

MANICALAND STATE UNIVERSITY OF APPLIED SCIENCES

FACULTY OF ENGINEERING, APPLIED SCIENCES AND TECHNOLOGY

Chemical Engineering Thermodynamics CHEP 121 Lecture Notes: First Law of Thermodynamics By Muhezwa C.

Internal Energy and the First Law of Thermodynamics

• Molecules in motion possess:
  • Kinetic Energy:
  • Types: translation, rotation, internal vibration.
  • Potential Energy:
  • Due to intermolecular forces (attraction or repulsion between molecules).
• Internal Energy (U):
  • Sum of total kinetic energy from molecular motion and potential energy from intermolecular forces.
  • Excludes energy from the gross position or movement of the system as a whole.
• While determining absolute internal energy is challenging, only changes in internal energy matter for thermodynamic analysis.

Representation of the First Law of Thermodynamics

• The First Law, or Principle of Conservation of Energy, states that:
  • Total energy of a system and its surroundings is constant.
  • Energy appears in different forms but total quantity remains fixed.
  • Energy transitions (one form disappearing and another appearing) are constant.
• Initially a postulate; has become a recognized law due to strong experimental evidence.

The First Law of Thermodynamics

• Statement: The total energy of any system and its surroundings is conserved.
• Definitions:
  • System: The portion of the universe chosen for analysis; includes everything within its boundaries.
  • Surroundings: Everything outside the system.
• Energy changes in the system may include changes in:
  • Internal energy
  • Potential Energy (PE)
  • Kinetic Energy (KE)
• Heat (Q) and Work (W):
  • Forms of energy in transit across system boundaries.
• Closed System:
  • No material transfer across boundaries; total energy change in surroundings equals heat and work exchanged with the system.

Mathematical Expressions in Thermodynamics

• For closed systems, energy balance equations are:
  • Change in energy of surroundings: $ext{∆(Energy of Surroundings)} = ±Q ± W$ …………(3.1)
  • Change in energy of the system: $ext{∆(Energy of System)} = ∆KE + ∆PE + ∆U$ ………. (3.2)
• Combining equations yields the First Law for Closed Systems:
  • $∆KE + ∆PE + ∆U = ±Q ± W$ …………(3.3)

Sign Convention

• Adopting Sign Convention:
  • Heat transferred to the system from surroundings is positive.
  • Work done by the system to surroundings is negative.
• Equation (3.3) modifies to:
  • $∆KE + ∆PE + ∆U = Q - W$ ………… (3.4)
• If changes in KE & PE are negligible:
  • $∆U = Q - W$ …………(3.5)
• For differential changes:
  • $dU = δQ - δW$ …………(3.6)

Internal Energy: Implications on the First Law

• Internal Energy (U) is a state function:
  • Path independence when computing $Q - W$, depending only on initial and final states.
• Useful in calculating energy requirements for processes in:
  • Heat exchangers, pumps, compressors, distillation columns, etc.
• State functions like U can be tabulated for any process, utilizing thermodynamic principles productively.

Thermodynamic Processes

• A system can experience various thermodynamic changes, adjusting Pressure (P), Volume (V), and Temperature (T).
• PV Diagram Representation:
  • Work done under PV curves is equivalent to the area under the curve:
  • W > 0 for expansion
  • W < 0 for compression.

Isothermal Process

• Definition: Process occurring at constant temperature (ΔT = 0).
• Assumption: System remains in contact with a heat reservoir, ensuring thermal equilibrium is maintained.
• For Ideal Gases:
  • Since $ΔT$ is zero, then $ΔU = 0$, thus:
  • From the First Law, $Q = W$
  • Any energy entering (Q) must leave as work (W).

Isothermal Process on a P-V Diagram

• Visualization:
  • Includes states A and B at constant temperature T1.
• Equation for work in an isothermal process:
  • $W=-Q$, reflecting energy conservation.

Iso-volumetric Process (Isochoric)

• Definition: Constant volume process.
• Work: No volume change implies:
  • $W = 0$
• Internal energy change relation:
  • $ΔU = Q$ (energy transferred is entirely as heat).
• Example: Heating gas in a closed, rigid container.

Iso-volumetric Process on a P-V Diagram

• Illustration:
  • Volume remains constant; process denoted by the same point on the curve.
• Similarly, Work remains zero (W = 0) and Heat is equal to the internal energy change.

Adiabatic Process

• Definition: Process with no heat exchange (Q = 0).
• Relation between changes:
  • $– ΔU = W ext{ or } ΔU = -W$
• Conditions for expansion and compression:
  • Expansion: Work done by the system (W positive) implies $ΔU$ is negative.
  • Compression: Work done on the system (W negative) thus $ΔU$ is positive.

Adiabatic Process on a P-V Diagram

• Visual Representation:
  • Notable isotherms and adiabat relationship:
  • Work effect shown during volumetric changes.

Isobaric Process

• Definition: Process occurring at constant pressure.
• Energy changes (ΔU, W, Q) can be non-zero:
  • Work from ideal gas calculated as: $W = P ΔV$
• Everyday example: Water boiling in a saucepan, reflecting constant pressure.

Isobaric Process on a P-V Diagram

• Demonstration:
  • Work calculated as $W = -P(V2 - V1)$
• Pressure remains constant; changes in volume occur under work done.

Enthalpy (H)

• Definition: Enthalpy is defined as: $H ≡ U + PV$ ……………………………(1)
  • Represents internal energy plus the product of pressure and volume.
• Enthalpy is a state function as all the contributing factors are state functions.
• The differential form is expressed as:
  • $dH = dU + d(PV)$
• Integrated form from equation (1):
  • $ΔH = ΔU + pΔV$ when transformed during constant pressure.
• At constant pressure, heat Q can be stated as:
  • Therefore for processes under constant pressure: $ΔH = Q$.
• An advantage of knowing enthalpy is its usefulness in energy balances for processes such as:
  • Heat exchangers, chemical reactors, pumps, turbines, etc.

Example on Calculation of ΔU and ΔH

• Calculating for 1 kg of water vaporized at 100°C and 101.33 kPa:
  • Change identified by specific volumes of liquid (0.00104 m³·kg⁻¹) and vapor (1.673 m³·kg⁻¹).
• Energy addition: $Q = 2256.9 kJ$
• Using Formulas:
  • $ΔH = Q = 2256.9 kJ$
  • For $ΔU$ using pressure-volume work:
  • $PAV = 101.33 ext{kPa} imes (1.673 - 0.001) ext{m}^3 = 169.4 ext{kJ}$
  • Thus, calculating internal energy:
  • $ΔU = 2256.9 - 169.4 = 2087.5 ext{kJ}$

Heat Capacity

• Definition: Heat capacity is categorized into two types for homogeneous fluids:
  • C₍V₎: Heat capacity at constant volume, defined as:
  • $C_V = \frac{3}{2} R$.
  • C₍P₎: Heat capacity at constant pressure, defined as:
  • $C_P = \frac{5}{2} R$.
• For constant volume processes:
  • $Q = nC_VΔT = ΔU$.
• The universal gas constant: $R = 8.314 ext{J/mol·K}$.

Heat Capacity at Constant Volume

• Heat capacity derivation considers state functions CVS with respect to Temp and Volume:
  • $ΔU = C_V(T_2 - T_1)$.
• No process dependency means C_V is independently evaluated.

Heat Capacity at Constant Pressure

• Definition encompasses both molar and specific heat capacities regarding enthalpy H:
  • $ΔH = C_P (T_2 - T_1)$,
• C_P serves as a state function that doesn't vary with the process.

Equations of State and Heat Capacities

• Case Study: N₂ gas at 273 K and 1 atm; adding 3000 J of heat causes 832 J of work:
  • Tasks include:
  • (i) Final state of the gas
  • (ii) Values for $ΔU$ and $ΔH$ during state change
  • (iii) Values of specific heat capacities c₍V₎ and c₍P₎ for N₂ assuming ideal gas behavior, reversible change of state.