Thermodynamics

Thermodynamics

Thermodynamics deals with heat, work, and internal energy. It is fundamental for understanding energy conversion and thermal effects on structures.

Temperature and Heat

Temperature ($T$): A measure of the average kinetic energy of particles in a substance.

• Kelvin (K): The absolute temperature scale. $T_K = T_C + 273.15$.
• Celsius ($^\circ$C): Common scale.

Heat ($Q$): The transfer of thermal energy between systems due to a temperature difference. $Q = mc \Delta T$ where $m$ is mass and $c$ is specific heat capacity. Unit: Joule (J) or Calorie (cal).

Thermal Expansion

Most materials expand when heated and contract when cooled.

• Linear Expansion: $\Delta L = \alpha L_0 \Delta T$
• Volume Expansion: $\Delta V = \beta V_0 \Delta T$

where $\alpha$ is the coefficient of linear expansion and $\beta \approx 3\alpha$ is the coefficient of volume expansion.

Civil Engineering Importance: Bridges and concrete pavements must have expansion joints to accommodate thermal expansion, preventing buckling and cracking. For example, steel has $\alpha \approx 12 \times 10^{-6} /^\circ$C, meaning a 100m bridge expands by 1.2 cm for a $10^\circ$C rise.

Laws of Thermodynamics

Zeroth Law

If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This defines temperature.

First Law (Conservation of Energy)

The change in internal energy ($\Delta U$) of a system is equal to the heat added to the system minus the work done by the system. $\Delta U = Q - W$

Second Law

Heat flows spontaneously from a hotter body to a colder body. It is impossible to convert heat completely into work in a cycle. Entropy ($S$) of an isolated system always increases. $\Delta S \ge 0$

Third Law

The entropy of a perfect crystal at absolute zero (0 K) is zero.

Heat Transfer Mechanisms

1. Conduction: Transfer of heat through direct contact (e.g., heat flow through a wall). $H = \frac{dQ}{dt} = -kA \frac{dT}{dx}$ where $k$ is thermal conductivity.

2. Convection: Transfer of heat by fluid motion (e.g., wind cooling a building). $H = hA(T_s - T_f)$

3. Radiation: Transfer of heat by electromagnetic waves (e.g., solar heating). $P = \sigma A \epsilon T^4$ Stefan-Boltzmann Law.