1. Fundamental Concepts
Thermodynamics is the study of energy, heat, work, and the macroscopic variables
that describe physical systems.
Systems and Boundaries
To analyze a problem, we must first define the System (the object of study) and the
Surroundings (everything else).
•
Open System: Can exchange both mass and energy with surroundings (e.g.,
an open boiler).
•
Closed System: Can exchange energy (heat/work) but not mass (e.g., gas in a
piston).
•
Isolated System: Cannot exchange mass or energy (e.g., an ideal vacuum
flask).
State Variables
•
Intensive Properties: Independent of the amount of matter (e.g., Temperature
$T$, Pressure $P$, Density $\rho$).
•
Extensive Properties: Proportional to the system size (e.g., Volume $V$, Mass
$m$, Internal Energy $U$).
2. The Four Laws of Thermodynamics
The Zeroth Law: Thermal Equilibrium
"If two systems are each in thermal equilibrium with a third system, they are in
thermal equilibrium with each other."
This law provides the logical basis for the concept of Temperature. It allows us to
use thermometers to measure and compare the "hotness" of different bodies.
The First Law: Conservation of Energy
Energy cannot be created or destroyed, only transformed. For a closed system, the
change in internal energy is the heat added minus the work done by the system.
$$dU = \delta Q - \delta W$$
•
$dU$: Change in internal energy (State function).
•
$\delta Q$: Heat transfer into the system (Path function).
•
$\delta W$: Work done by the system ($P dV$ work) (Path function).
The Second Law: Entropy and Directionality
Not all energy transfers are possible. Heat spontaneously flows from hot to cold,
never the reverse without external work.
•
Entropy ($S$): A measure of molecular disorder or energy unavailability.
•
Clausius Statement: For any spontaneous process in an isolated system, the
total entropy always increases.
$$dS \ge \frac{\delta Q}{T}$$
The Third Law: Absolute Zero
"As the temperature of a system approaches absolute zero ($0 \text{K}$), the
entropy of a perfect crystal approaches zero."
This implies that it is impossible to reach absolute zero in a finite number of steps.
3. Thermodynamic Potentials
These functions are essential for predicting the equilibrium state and the
spontaneity of reactions.
Potential
Internal Energy ($U$)
Enthalpy ($H$)
Helmholtz Free Energy
($A$)
Formula
$dU = T dS - P
dV$
$H = U + PV$
$A = U - TS$
Gibbs Free Energy ($G$) $G = H - TS$
Common Use
Fundamental energy balance.
Heat flow in constant pressure
processes.
Useful for constant $T$ and
$V$ systems.
Predicts spontaneity at constant
Potential
Formula
Common Use
$T$ and $P$.
Spontaneity Tip: A process is spontaneous if $\Delta G < 0$ at constant
temperature and pressure.
4. Key Thermodynamic Processes
1. Isobaric ($P$ is constant): $W = P(V_2 - V_1)$.
2. Isochoric ($V$ is constant): $dV = 0 \rightarrow W = 0$. All heat added goes
into internal energy ($dU = dQ$).
3. Isothermal ($T$ is constant): For an ideal gas, $dU = 0 \rightarrow dQ =
dW$.
4. Adiabatic ($Q = 0$): No heat exchange. Described by the relation
$PV^\gamma = \text{constant}$ (where $\gamma$ is the heat capacity
ratio).
5. Maxwell Relations
Derived from the exact differentials of thermodynamic potentials, these allow us to
relate non-measurable quantities (like entropy) to measurable ones (like $P, V, T$).
•
$(\frac{\partial T}{\partial V})_S = -(\frac{\partial P}{\partial S})_V$
•
$(\frac{\partial T}{\partial P})_S = (\frac{\partial V}{\partial S})_P$
•
$(\frac{\partial S}{\partial V})_T = (\frac{\partial P}{\partial T})_V$
•
$(\frac{\partial S}{\partial P})_T = -(\frac{\partial V}{\partial T})_P$