Entropy – 2^{nd} Law

Definition of thermodynamic efficiency:

or

Consider a Carnot cycle: (page 157 5^{th} Ed.)

For the isothermal steps:

A)

B)

From the adiabatic steps:

Since and

Integrating a® b or c® d:

Then:

From A) & B):

Substitution for N_{eqn}:

Arbitrary work path:

__Clauusius’ theorem__ – any process can be broken into equivalent isothermal
& adiabatic steps!

Therefore as before we can sum over the cycle:

or for many tiny cycles to sum up:

Over less than a whole cycle the integral may not be zero;

Then:

or

- Entropy is a state function, & therefore, although we calculate D S from a hypothetical reversible process, it is identical in an equivalent irreversible process.
- Entropy of the universe is not conserved:

Combined 1^{st} & 2^{nd} Law

- Energy conserved – 1
^{st}Law(neglect PE & KE)

- Entropy is defined as: 2
^{nd}Law - Combined 1
^{st}& 2^{nd}Law:

Substitute for dQ

or

or

Ideal Gasses & 2^{nd} Law

1) Constant volume process:

- Constant Pressure processes:

.

- Constant temperature process:
- Going from P
_{1}V_{1}T_{1}to P_{2}B_{2}T_{2}:

Or
in terms of T, V: (T_{1}V_{1® }T_{2}V_{2})

P, V: (P_{1}V_{1® }P_{2}V_{2})

Since D S is a state function these can be used
for __any__ __path__!

Adiabatic reversible processes

Isentropic process!