B.4 Thermodynamics (HL only)

Picture this: you're inflating a bicycle tire with a pump and notice the pump gets warm. Why does compressing a gas raise its temperature? The answer lies in thermodynamics , the study of energy, heat, and their transformations.

Internal Energy (U): The total energy stored within a thermodynamic system , for a gas, this is the sum of the random kinetic energy of all particles and the potential energy from intermolecular forces.

For a monatomic ideal gas, intermolecular forces are assumed to be zero, so internal energy is entirely kinetic:

$U=\frac{3}{2}N{k}_{B}T$

where:

• $N$ = number of gas particles
• $k_B=1.38\times 10^{-23}{\text{J K}}^{-1}$ (Boltzmann constant)
• $T$ = absolute temperature in kelvin

Using $PV=nRT$, this can also be written as:

$U=\frac{3}{2}nRT=\frac{3}{2}PV$

This reveals a crucial point: the internal energy of an ideal gas depends only on its temperature, not on pressure or volume independently.

In thermodynamics, we define a system as the specific region or collection of matter under study. Everything outside is the surroundings.

Systems are classified by what they can exchange with their surroundings:

State Function: A property whose value depends only on the current state of the system (described by variables like $P$, $V$, $T$), not on the path taken to reach that state.

Internal energy $U$ is a state function. This means:

$\Delta U=U_{\text{final}}-U_{\text{initial}}$

regardless of how the system got from one state to the other.

In contrast, heat ($Q$) and work ($W$) are NOT state functions , they describe energy in transit during a process and depend on the path taken.