# SL: The need for the second law

### The need for the Second Law of Thermodynamics

Processes have directionality:

##### Example:

An 100g ice cube at -10C is added to a 500g cup of coffee at 80C in an insulated (adiabatic) cup. What will happen? Perform a first law analysis of this process to obtain the final temperature.

##### Example:

A 600 g cup of lukewarm coffee in an insulated (adiabatic) cup is made to separate into a 100 g cube of ice at -10C and 500 ml of 80C coffee. Perform a first law analysis.

##### Observation:

Thermal directionality: heat goes from high T to low

##### Example:

Two gases at 100C and 1 atm -- water/steam and ethanol -- are in either side of a partitioned box. What will happen when the partition between water and ethanol is opened.

##### Example:

Gasoline and oxygen are mixed in a container at 500C. What do you expect will happen? What if they are mixed at 2000C? How about 25C?

##### Observation:

Chemical directionality: concentration gradients and chemical potential "gradients" get "smoothed out".

##### Example:

A partition divides a box in half. One half contains 100 molecules of nitrogen; the other half is empty. What will happen if a hole is made in the partition? How many molecules will be in each half when the system comes to equilibrium?

##### Observation:

Mechanical directionality: pressure gradients drive flow.

##### Note:

Conservation of mass + conservation of energy (first law) are exact but incomplete $\rightarrow$ No inherent direction; Spontaneity is not predicted. Need something else