2nd Law | Sahithyan's Notes

Heat will not spontaneously flow from a colder body to a hotter body. Establishes the concept of entropy $S$ as a measure of disorder or randomness in a system. Natural processes tend to move toward states of higher entropy.

Entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

Entropy

The Clausius inequality:

\text{d}S \geq \frac{\delta Q}{T}

Here:

$\delta Q$ : differential heat transfer into the system
$T$ : absolute temperature at the boundary

Equality holds for reversible processes. Strict inequality holds for irreversible processes.

Entropy Change

For a reversible process:

\Delta S = \int_1^2 \frac{\delta Q}{T}

For a reversible isothermal process at temperature $T$ :

\Delta S = \frac{Q}{T}

For an isolated system: $\Delta S \geq 0$ .

Thermal Reservoir

Aka. heat reservoir. A body that can either absorb or release heat at constant temperature. Isothermal heat transfer device.

Sink

A thermal reservoir that absorbs heat.

Source

A thermal reservoir that releases heat.

Kelvin-Planck Statement

It is impossible for any device that operates on a cycle to exchange heat with a single reservoir and produce a net amount of work. Explains the operational constraints of a heat engine.

Clausius Statement

It is impossible to construct a system which will transfer heat from a cooler body to a hotter body without work being done on the system by surrounding.

Establishes the operational constraints of heat pumps and refrigerators.