Thermodynamics: Zeroth & First Law

Thermodynamics

• Focuses on heat transfer and related phenomena.
• Concentrates on both thermal equilibrium and heat transfer.

Zeroth Law of Thermodynamics

• If objects A and B are separately in thermal equilibrium with object C, A and B are in thermal equilibrium with each other.

First Law of Thermodynamics

• Internal Energy (U) is the energy associated with the microscopic components of a system, including the kinetic and potential energy of atoms and molecules.
• Only changes in internal energy are relevant.
• Internal Energy is a state variable that depends only on the state of the system, not the path taken to get there.
• U is therefore, path independent.
• Heat (Q) is the transfer of energy across a system's boundary due to a temperature difference between the system and surroundings; its units are in Joules (J).
• Heat is positive when energy enters the system and negative when energy exits the system.
• Work (W) is the transfer of energy when a force displaces a particle
• A quasi-static process occurs slowly enough for the system to remain in internal equilibrium.
• $dW=F \cdot dr=PAdx=PdV$
• $W = \int_{i}^{f}PdV$
• Units are in Joules (J).
• Work is positive when energy is transferred out of the system, and negative when energy is transferred into the system.
• The change in a system's internal energy is equal to the heat added to the system minus the work done by the system: $\Delta U = Q - W$ or $dU = dQ - dW$.

Types of Thermodynamic Processes

• Adiabatic processes involve no heat transfer $(Q = 0)$, so $\Delta U = -W$.
• Isobaric processes occur at constant pressure, with $W = P(V_{f} - V_{i})$.
• Isovolumetric processes occur at constant volume, meaning $W = 0$ and $\Delta U = Q$.
• Isothermal processes occur at constant temperature, meaning $\Delta U = 0$ and $Q = W$; for an ideal gas: $W = n R T \ln\left(\frac{V_{f}}{V_{i}}\right)$.

Heat Engines and the Second Law of Thermodynamics

• Heat engines convert thermal energy into other forms of energy, taking in energy by heat and partially converting it, usually in a cyclic process.
• Second Law of Thermodynamics: No heat engine can convert energy from heat into mechanical work with 100% efficiency
• Efficiency of a heat engine is defined as: $e = \frac{W_{\text{net}}}{Q_{h}} = 1 - \frac{Q_{c}}{Q_{h}}$ where $Q_{h}$ is the energy taken in from the hot reservoir and $Q_{c}$ is energy expelled to the cold reservoir.

Carnot Engine

• Carnot Engine: The most efficient heat engine possible.
• $e_{c} = 1 - \frac{T_{c}}{T_{h}}$
• All real engines are less efficient than a Carnot engine.
• Carnot Cycle stages:
  • Isothermal Expansion
  • Adiabatic Expansion
  • Isothermal Compression
  • Adiabatic Compression

Entropy

• Entropy measures the disorder of a system; higher disorder corresponds to higher entropy.
• Entropy is a state variable.
• S is path independent.

Change in Entropy Formula

• Change in entropy is equal to the heat added to the system divided by the temperature: $\Delta S = \int_{i}^{f} \frac{dQ}{T}$. For a reversible process: $\Delta S = \frac{Q}{T}$.
• Units: J/K

Second Law of Thermodynamics (Entropy)

• Entropy: the total entropy of an isolated system always increases in time.
• Approximated in reality by the Universe.
• $\Delta S_{\text{universe}} \geq 0$ The entropy of the Universe is always increasing!
• Processes that decrease entropy are not spontaneous.
• Entropy can decrease locally, but must increase elsewhere by at least as much.
• The Second Law of Thermodynamics explains the "arrow of time".
• The Universe was more ordered in the past.
• Probability of a system being disordered is higher than the probability of it being ordered.
• Entropy is related to probability.