Chapter Review

Heat and Thermodynamics

Heat, Work, Internal Energy and First Law · Specific Heat, Molar Specific Heat and Cp-Cv Relation

First Law of Thermodynamics

Energy conservation applied to thermodynamic systems: the net heat added minus the work done by the system equals its change in internal energy.

Key Points

  • •
    Internal energy is a state function (depends only on current state), while and are path functions
  • •
    Sign convention: = heat added to system, = work done BY system; work done ON system makes negative
  • •
    For ideal gases, internal energy depends only on temperature
  • •
    All three quantities (, , ) have units of joules — always verify unit consistency
Formula

Isothermal and Adiabatic Processes

Two fundamental thermodynamic processes where one variable is held constant, leading to distinct energy relationships and PV diagram curves.

Key Points

  • •
    Isothermal: so ; Boyle's Law applies; must occur slowly for heat exchange
  • •
    Adiabatic: so ; expansion cools the gas, compression heats it; occurs rapidly or in insulated systems
  • •
    Adiabatic curve is steeper than isothermal on a PV diagram because both and decrease during expansion
  • •
    Real examples: bicycle pump (adiabatic compression → heating), burst tyre (adiabatic expansion → cooling), cloud formation
Formula

Isochoric Process and First Law Special Cases

When the process constrains a variable, the first law reduces to simpler forms that reveal direct relationships between heat, work, and internal energy.

Key Points

  • •
    Isochoric (constant volume): , so — all heat stored as internal energy
  • •
    Isothermal: , so — all heat converts to work
  • •
    Adiabatic: , so — work done at expense of internal energy
  • •
    These three cases are the most commonly tested applications of the first law

Heat Engines and Thermal Efficiency

A heat engine converts thermal energy into mechanical work by cycling between a hot and cold reservoir, with efficiency determined by the fraction of input heat converted to work.

Key Points

  • •
    Engine operates in cycles so and
  • •
    Efficiency — always compare work to heat INPUT, not waste heat
  • •
    Real-world efficiencies: petrol engines 25-30%, diesel 35-40%, steam turbines 35-46%
  • •
    Diesel engines are more efficient due to higher compression ratios; they use compression ignition instead of spark plugs
Formula

Second Law and the Carnot Cycle

The second law forbids 100% heat-to-work conversion. The Carnot cycle — an ideal reversible cycle — sets the theoretical maximum efficiency for any heat engine operating between two temperatures.

Key Points

  • •
    Kelvin statement: impossible to extract heat from a single reservoir and convert it entirely to work
  • •
    Carnot efficiency depends only on reservoir temperatures in Kelvin, not on the working substance
  • •
    Shortcut: if then ; if then
  • •
    To raise efficiency practically, increase (since is usually near room temperature)
  • •
    Must use Kelvin in the Carnot formula — never °C
  • •
    Carnot cycle steps: isothermal expansion at , adiabatic expansion, isothermal compression at , adiabatic compression
Formula

Entropy

Entropy measures the unavailability of a system's energy to do work, and the second law guarantees that total entropy of the universe always increases in natural processes.

Key Points

  • •
    when heat added, when heat removed
  • •
    For heat flowing from to : (always positive)
  • •
    Same at low produces larger entropy change than at high
  • •
    Phase transitions: melting and boiling increase entropy; freezing and condensation decrease it
  • •
    Total entropy is conserved in reversible processes but increases in all irreversible ones
Formula

Reversible vs Irreversible Processes

Reversible processes are idealizations that can be retraced without changing the surroundings, setting the upper bound on efficiency. All real processes are irreversible.

Key Points

  • •
    Reversible: slow compression, slow evaporation/condensation — maintained in thermal and mechanical equilibrium
  • •
    Irreversible: explosions, friction, rapid heat transfer, free expansion — involve dissipation
  • •
    Reversible processes produce zero net entropy change
  • •
    Irreversible processes increase total entropy of the universe
  • •
    A thermodynamic cycle returns the system to its initial state; reversible cycles have all reversible steps

Specific Heat, Molar Specific Heat and Cp-Cv

The heat capacity of a gas differs depending on whether it is heated at constant pressure or constant volume, linked by the universal gas constant through the Cp-Cv relation.

Key Points

  • •
    Specific heat is heat per unit mass per degree; molar specific heat is heat per mole per degree
  • •
    because at constant pressure, extra heat goes into expansion work (not just raising temperature)
  • •
    Mayer's relation: (where J/mol·K is the universal gas constant)
  • •
    The ratio appears in the adiabatic condition
  • •
    Monatomic ideal gas: , ,
  • •
    Diatomic ideal gas: , ,
Formula

Thermodynamic Temperature Scale

The Kelvin scale defined via the Carnot cycle provides a temperature measurement independent of any material's properties, anchored at the triple point of water.

Key Points

  • •
    Triple point of water: 273.16 K — where ice, liquid water, and water vapour coexist in equilibrium
  • •
    1 K is defined as 1/273.16 of the triple-point temperature
  • •
    Unlike mercury or alcohol thermometers, this scale does not depend on any substance's expansion
  • •
    All thermodynamic formulas (Carnot efficiency, entropy) require temperatures in Kelvin
Formula

Formulas

First Law of Thermodynamics

Energy balance: heat in minus work out equals change in internal energy.

Isothermal Process

Boyle's Law — pressure and volume are inversely proportional at constant temperature.

Adiabatic Condition

Pressure-volume relation when no heat is exchanged ($Q = 0$).

Thermal Efficiency

Useful work output divided by total heat energy input.

Carnot Efficiency

Maximum possible efficiency depends only on reservoir temperatures in Kelvin.

Mayer's Relation

Difference between molar specific heats at constant pressure and constant volume equals the gas constant.

Entropy Change

Heat transferred divided by absolute temperature at which transfer occurs.

Work Done by Gas

Work at constant pressure equals pressure times change in volume.