Key Points

If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This law establishes the concept of temperature as a fundamental property.

Internal energy (U) is the sum of molecular kinetic and potential energies and is a state variable. Heat (Q) and Work (W) are modes of energy transfer and are path-dependent, not state variables.

This is the law of conservation of energy, expressed as $\Delta Q = \Delta U + \Delta W$. Here, $\Delta Q$ is the heat supplied to the system, $\Delta U$ is the change in its internal energy, and $\Delta W$ is the work done by the system.

Equilibrium states are described by state variables like Pressure (P), Volume (V), and Temperature (T), whose values depend only on the state itself, not how it was reached. An equation of state, like $PV = \mu R T$ for an ideal gas, connects these variables.

Molar specific heat at constant pressure ($C_p$) and constant volume ($C_v$) measure the heat needed to raise the temperature of one mole of a substance. For an ideal gas, they are related by Mayer's formula: $C_p - C_v = R$.

A quasi-static process is an idealized, infinitely slow process where the system remains in thermal and mechanical equilibrium with its surroundings at every stage. It is a necessary condition for a process to be reversible.

An isothermal process occurs at a constant temperature ($\Delta T = 0$). For an ideal gas, internal energy does not change ($\Delta U = 0$), so heat supplied equals work done: $Q = W = \mu R T \ln(\frac{V_2}{V_1})$.

An adiabatic process occurs with no heat transfer between the system and surroundings ($\Delta Q = 0$). For an ideal gas, it follows the relation $PV^\gamma = \text{constant}$, where $\gamma = \frac{C_p}{C_v}$.

The work done by an ideal gas during an adiabatic change from state $(T_1, V_1)$ to $(T_2, V_2)$ is $W = \frac{\mu R(T_1 - T_2)}{\gamma - 1}$. This work is done at the expense of the internal energy.

In an isochoric process, volume is constant ($\Delta V = 0$), so no work is done. In an isobaric process, pressure is constant, and work done is $W = P(V_2 - V_1)$.

This law sets direction for natural processes. The Kelvin-Planck statement says 100% heat-to-work conversion is impossible. The Clausius statement says heat cannot spontaneously flow from a colder to a hotter body.

A reversible process can be reversed to restore the initial states of both the system and surroundings. All real-world processes are irreversible due to dissipative forces like friction or non-equilibrium conditions.

The Carnot engine is an ideal, reversible heat engine that operates in a cycle of two isothermal and two adiabatic processes. It has the maximum possible efficiency for any engine operating between two given temperatures.

The efficiency ($\eta$) of a Carnot engine depends only on the absolute temperatures of the hot source ($T_1$) and the cold sink ($T_2$). The formula is $\eta = 1 - \frac{T_2}{T_1}$.