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HSSLIVE Plus One Physics Chapter 12: Thermodynamics Notes

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Thermodynamics introduces students to the laws governing energy transfer and transformation in physical systems. Students explore the zeroth, first, and second laws of thermodynamics to understand thermal equilibrium, conservation of energy, and entropy. This chapter applies these concepts to heat engines, refrigerators, and heat pumps, connecting theoretical limits to real-world efficiency challenges in energy conversion technologies that power our modern world.

Chapter 12: Thermodynamics

1. Thermal Equilibrium and Zeroth Law

Thermodynamic equilibrium refers to a state where a system has no tendency to change its macroscopic properties over time. Thermal equilibrium specifically refers to the condition where two systems have the same temperature and there’s no net heat flow between them when they’re in contact.

The Zeroth Law of Thermodynamics states: If two systems A and B are each in thermal equilibrium with a third system C, then A and B are in thermal equilibrium with each other. This law provides the basis for temperature measurement and the concept of temperature as a physical quantity.

A thermodynamic system can be:

  • Isolated system: No exchange of energy or matter with surroundings
  • Closed system: Exchange of energy but not matter
  • Open system: Exchange of both energy and matter

2. First Law of Thermodynamics

The First Law of Thermodynamics is essentially the law of conservation of energy applied to thermodynamic systems. It states that energy can neither be created nor destroyed, only transformed from one form to another.

Mathematically:

  • ΔU = Q – W
  • Where ΔU is change in internal energy, Q is heat added to the system, and W is work done by the system

Internal energy (U) is the total energy contained within a system, including kinetic and potential energies of molecules. For an ideal gas, U depends only on temperature, not on pressure or volume.

The sign convention is important:

  • Q is positive when heat is added to the system
  • W is positive when work is done by the system
  • If the system does work (expansion), W is positive
  • If work is done on the system (compression), W is negative

3. Specific Heat Capacity in Thermodynamic Processes

The specific heat capacity depends on the conditions under which heating occurs:

Specific heat capacity at constant volume (C_v):

  • Q = nC_vΔT (for n moles)
  • No work is done (ΔV = 0, so W = 0)
  • Therefore, ΔU = Q = nC_vΔT

Specific heat capacity at constant pressure (C_p):

  • Q = nC_pΔT (for n moles)
  • Work is done by gas expansion (W = PΔV)
  • For ideal gas, C_p – C_v = R (gas constant)
  • C_p is always greater than C_v because at constant pressure, additional heat is needed for expansion work

For monoatomic gases, C_v = 3R/2 and C_p = 5R/2 For diatomic gases at room temperature, C_v = 5R/2 and C_p = 7R/2

4. Thermodynamic Processes

Thermodynamic processes are paths through which a system changes from one state to another:

Isothermal Process (constant temperature, ΔT = 0):

  • For ideal gas: PV = constant (Boyle’s Law)
  • Internal energy doesn’t change (ΔU = 0)
  • Therefore, Q = W (heat added equals work done)
  • Work done: W = nRT ln(V₂/V₁)

Adiabatic Process (no heat exchange, Q = 0):

  • For ideal gas: PV^γ = constant (where γ = C_p/C_v)
  • First law gives: ΔU = -W (internal energy change equals negative of work done)
  • Work done: W = [P₁V₁ – P₂V₂]/(γ-1)
  • Temperature change: T₂/T₁ = (V₁/V₂)^(γ-1)

Isochoric/Isovolumetric Process (constant volume, ΔV = 0):

  • No work is done (W = 0)
  • First law gives: ΔU = Q (all heat goes to internal energy)
  • Q = nC_vΔT

Isobaric Process (constant pressure, ΔP = 0):

  • Work done: W = PΔV
  • Q = ΔU + W = nC_vΔT + PΔV = nC_pΔT

5. Heat Engines and Efficiency

A heat engine is a device that converts thermal energy into mechanical work by extracting heat from a high-temperature reservoir and rejecting some of it to a low-temperature reservoir.

The efficiency of a heat engine is the ratio of useful work output to heat input:

  • Efficiency (η) = W/Q_H = (Q_H – Q_C)/Q_H = 1 – Q_C/Q_H
  • Where Q_H is heat absorbed from hot reservoir and Q_C is heat rejected to cold reservoir

No heat engine can have 100% efficiency because some heat must always be rejected to a cold reservoir (Second Law of Thermodynamics).

6. Second Law of Thermodynamics

The Second Law can be stated in several equivalent ways:

Kelvin-Planck statement: No process is possible whose sole result is the extraction of heat from a reservoir and its complete conversion into work.

Clausius statement: No process is possible whose sole result is the transfer of heat from a colder to a hotter body.

The Second Law introduces the concept of entropy (S), a measure of disorder or randomness:

  • For reversible process: ΔS = Q/T
  • For any process: ΔS ≥ Q/T
  • For isolated system: ΔS ≥ 0 (entropy never decreases)

7. Carnot Engine and Refrigerators

The Carnot engine is an ideal heat engine operating in a reversible cycle between two temperature reservoirs. It consists of two isothermal and two adiabatic processes.

The efficiency of a Carnot engine depends only on the temperatures of the reservoirs:

  • η_carnot = 1 – T_C/T_H
  • This represents the maximum possible efficiency for any engine operating between these temperatures

Refrigerators and heat pumps are essentially heat engines running in reverse. They use work to extract heat from a cold reservoir and reject it to a hot reservoir:

  • Coefficient of Performance (refrigerator) = Q_C/W
  • Coefficient of Performance (heat pump) = Q_H/W

Carnot’s theorem states that no engine can be more efficient than a Carnot engine operating between the same temperatures, making it a fundamental benchmark in thermodynamics.

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