Thermodynamics

Thermodynamic equilibrium is characterized by **macroscopic** state variables like pressure, volume, and temperature. These are time-independent in equilibrium.

At , water exhibits anomalous expansion, meaning that its volume does not change with temperature under constant pressure: Since the heat capacities are related by:
when , it follows that .

A quasi-static process is one in which the system changes infinitesimally slowly, ensuring that it remains arbitrarily close to thermodynamic equilibrium at all times.

The work done in a thermodynamic process is given by:
For 1 liter-atmosphere (L-atm):

The first law of thermodynamics states:
This equation implies:
- The existence of an internal energy function .
- The principle of conservation of energy, since heat added and work done must be accounted for.
- Heat is defined as energy transferred due to a temperature difference.

For an **adiabatic expansion of a black body**, the relation between temperature and volume is:
If the volume increases 64 times: Thus, the correct answer is:

The Joule-Kelvin coefficient is given by:
- Cooling occurs when (i.e., temperature decreases as pressure decreases).
- Heating occurs when (temperature increases as pressure decreases).
- At the inversion temperature, .

The isobaric volume expansivity and isothermal compressibility are related as:

For a Van der Waals gas, the internal energy depends only on temperature:
At constant temperature, the internal energy remains independent of volume.

For saturated steam, any heat added at constant pressure results in a phase change rather than a temperature increase. The definition of specific heat is:
Since temperature does not change during phase transition:
Thus, the correct answer is: