Thermo full_compressed

Thermodynamics

1. Introduction

Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. One of the fundamental principles is that the internal energy of a system is not directly measurable; only differences in internal energy can be observed, which is crucial for the analysis of thermodynamic processes.

2. First Law of Thermodynamics

The First Law of Thermodynamics, also known as the Law of Energy Conservation, states that energy cannot be created or destroyed in an isolated system.

• Conservation of Energy: This law relates heat (Q), internal energy (U), and work (W), stating that the total energy of a closed system remains constant.

• Clausius' Law: Heat energy converted into other forms maintains total energy and cannot be entirely transformed into work with no losses.

• Law Formulation: When heat (Q) is supplied to a system, a portion increases the internal energy (ΔU), and the remainder is utilized for external work (ΔW).

  • Equation: Q = ΔU + ΔW

  • Differential form: dQ = dU + dW

• Heat Conventions:

  • Positive (+):

    • Q: Heat is supplied to the system

    • ΔU: Internal energy increases

    • ΔW: Work is done by the system

  • Negative (-):

    • Q: System loses heat

    • ΔU: Internal energy decreases

    • ΔW: Work is done on the system

The change of internal energy is the difference between heat flow into the system and work done by it, illustrating the conservation of energy principle in thermodynamic processes.

3. Limitations of the First Law

Despite its importance, the First Law does not indicate the direction of heat flow. For example, processes such as the spontaneous melting of ice into water are not accounted for, highlighting the need for a more comprehensive understanding of thermodynamic principles.

4. Applications of the First Law

Thermodynamics allows us to analyze several processes, particularly those involving gases:

• Work Done by an Expanding Gas:

  • The p-V diagram (pressure-volume diagram) is essential for visualizing gas behavior under various conditions, known as the indicator diagram.

  • Isobaric Process: Pressure remains constant.

    • Work done (dW): dW = p dV

    • Total work: W = p(V₂ - V₁)

  • Isochoric Process: Volume remains constant.

    • Work done: dW = 0

    • The first law simplifies to: dQ = dU

  • Isothermal Process: Temperature remains constant.

    • Work done and heat exchange are equivalent: dQ = dW

  • Adiabatic Process: No heat exchange occurs.

    • Leads to: 0 = dU + dW or W = -dU.

    • Characterized by changes in internal energy affecting temperature without any heat transfer.

5. Specific Heat Capacity

Specific heat capacity is defined as the amount of heat needed to raise the temperature of a unit mass of a substance by one degree Celsius (or one Kelvin).

• Molar Specific Heat: Refers to the quantity of heat required to raise the temperature of one mole of a gas by one kelvin, specified either at constant pressure (Cₚ) or constant volume (Cᵥ).

• It is important to note that Cₚ > Cᵥ because additional work must be done against ambient pressure during heating at constant pressure.

6. Relation Between Cₚ and Cᵥ for Ideal Gas

For an ideal gas, the difference in specific heats is given by:

• Equation: Cₚ - Cᵥ = R, where R is the gas constant.

• The ratio of specific heats: γ = Cₚ / Cᵥ can be used to identify gas types and is significant in calculating the velocities of sound in gases.

7. Carnot's Engine

Carnot's Engine, conceived by Sadi Carnot, represents an ideal heat engine that operates in a reversible manner and is free from all imperfections.

• The efficiency of a Carnot cycle is determined by the temperature differences between the hot and cold reservoirs.

• Efficiency Equation: Efficiency = 1 - T₂/T₁, where T₁ is the absolute temperature of the hot reservoir and T₂ is the absolute temperature of the cold reservoir.

8. Second Law of Thermodynamics

The Second Law states that heat cannot be completely converted into work, indicating that not all heat energy can be effectively harnessed.

• This law describes the natural flow of heat and the inevitability of energy dissipation in various processes, which can be seen in everyday occurrences.

9. Refrigerators and Heat Pumps

Refrigerators operate in contrast to heat engines, requiring work input to transfer heat from lower temperature environments to higher ones.

• The efficiency of refrigerators is often expressed as the Coefficient of Performance (COP), which measures the effectiveness of heating or cooling systems.

10. Entropy

Entropy serves as a measure of disorder in a system, which tends to increase as systems progress toward thermal equilibrium.

• It is quantitatively defined as dS = dQ/T, indicating that entropy changes as a function of energy exchanges with temperature.

• The Carnot cycle allows for the examination of entropy changes during both reversible and irreversible processes, demonstrating that entropy increases in spontaneous processes, reflecting the arrow of time in thermodynamics.

Specific Heat Capacity ( C_p ) and ( C_v )

• Specific Heat Capacity: Amount of heat needed to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin).

• Molar Specific Heat: Heat required to raise the temperature of one mole of gas by one kelvin, at constant pressure ( C_p ) or constant volume ( C_v ).

• Relation: ( C_p > C_v ) due to additional work against ambient pressure during heating at constant pressure.

Relation Between (C_p) and (C_v) for Ideal Gases

• The difference in specific heats is given by the equation: ( C_p - C_v = R ) (where ( R ) is the gas constant).

• The ratio of specific heats is defined as ( \gamma = \frac{C_p}{C_v} ), which helps identify gas types and calculates sound velocities in gases.

Second Law of Thermodynamics

• Definition: States that heat cannot be completely converted into work, highlighting the limitations on energy efficiency in processes.

• Implication: Not all heat energy can be effectively utilized; it describes the tendency of heat to flow naturally from hot to cold bodies and the inevitability of energy dissipation.

• Applications: Addresses phenomena such as irreversible processes and the direction of spontaneous changes, emphasizing that systems evolve towards a state of increased disorder (entropy).

Carnot's Engine

• Concept: An idealized heat engine that operates under reversible processes, maximizing efficiency without imperfections.

• Efficiency: Determined by the temperature ratio of the hot and cold reservoirs, expressed as: ( \text{Efficiency} = 1 - \frac{T_2}{T_1} ), where ( T_1 ) and ( T_2 ) are the absolute temperatures of the hot and cold reservoirs respectively.

• Significance: Provides a baseline to evaluate real heat engines and demonstrates the maximum theoretical efficiency based on temperature limits.

Refrigerators and Heat Pumps

• Function: These devices operate contrary to heat engines, requiring work input to transfer heat from a lower temperature area to a higher temperature.

• Efficiency Measurement: Expressed as the Coefficient of Performance (COP), which indicates the effectiveness of the heating or cooling systems based on the heat removed or added relative to the work input.

• Applications: Essential in applications like climate control, food preservation, and industrial refrigeration, showcasing the principles of thermodynamics in practical scenarios.