Entropy is a measure of the quality of energy and how usable it is....

Entropy (S)is very difficult to visualise because it does not represent anything tangible.
The entropy increase δS is the heat transfer to a substance δQ divided by the absolute
temperature of the substance (T) during a __reversible__ heat-transfer process.

At the very simplest level , on a plot of Absolute Temperature (T) against Entropy
(Q/T = S) for a reversible cyclic process (as shown below) the area enclosed = Q

Note: The __reversible__ cyclic process shown below is actually the theoretical Carnot cycle.

1->2 being isothermal expansion.

2->3 being adiabetic expansion.

3->4 being isothermal compression.

4->1 being adiabetic compression.

The change in entropy ( δS ) of a substance is that quantity which when multiplied
by the absolute temperature at which the change took place results in the amount of energy ( δQ )
flow reversibly by heat transfer across the boundary enclosing the substance.

Total entropy is a property (extensive) of a substance and therefore the change in entropy
during a process, from an initial to a final state, is the same whatever the path taken. The change in entropy resulting from
any real (irreversible) process is the same as that resulting from a reversible process with
the same initial and final states. Therefore to determine the change in entropy
resulting from a real irreversible process an equivalent reversible process must be
envisaged to replace the real process from initial to final states before integration of the following

Typical SI units for total entropy (S) change are kJ /K.

SI units for specific entropy (s) change are kJ/kg.K

For an ideal constant volume process... (dQ = mc_{v}dT )

For an ideal constant pressure process... ( dQ = mc_{p}dT )

For an ideal adiabetic process...

For an ideal isothermal process...

There is no change in temperature and therefore there is no change in internal energy U.

From the first law of thermodynamic dQ = dU + dW. If dU = 0 then dQ = dW.

From the definition of entropy i.e δQ_{rev} = TδS

and from the first law of thermodynamics is dQ = dE + dW which, for a reversible process can be written as
δQ_{rev} =δE + PδV...

it can be
deduced that dE = TdS - PdV for a reversible process and if the substance is a gas of mass m then

For a perfect gas PV = mRT and assuming C_{v} is constant.

a) Entropy change in terms of V and T

b) Entropy change in terms of P and T

c) Entropy change in terms of P and V

To determine the entropy change in the irreversible adiabetic expansion of Joules experiment.... - In this experiment a gas at high pressure (properties P For an isothermal process the change in entropy = In this case although the process is adiabetic because it is not reversible it is not isentropic. There is
a resulting increase in entropy reflecting the various irreversible energy losses in this process |

Ideal reversible adiabetic and isothermal processes are straight lines on the TS chart as shown
above ac = ideal isothermal process and ab = ideal isentropic process. An adiabetic process
is one which is insulated against heat transfer and an isentropic process is one with a constant entropy.
δQ may be zero during a adiabetic process but if the process is not reversible then
δS = δQ /T does not apply and δS is not zero.

If the process is reversible then δQ = 0 and δS = 0 i.e the process is adiabetic
and isentropic.

A isentropic process is not necessarily reversible for a real expansion or compression-with all the associated
eddies and friction associated with real processes may have sufficient heat transfer to
maintain the entropy of the relevant substance constant (δS = 0 ). A real process
could be isentropic but would not at the same time be adiabetic because some heat transfer
would be necessary. The following relationships are possible

- In a real (irreversible) adiabetic process δQ = 0 but δS > 0
- In a reversible adiabetic process δQ = 0 and δS =0 0
- In a real (irreversible) isentropic process δS = 0 but δQ < 0
- In a reversible isentropic process δS = 0 and δQ = 0 0

- Entropy-wikipedia..Very detailed notes
- An Introduction to Entropy..Article reflecting a generalised view of entropy
- Hyperphysics Second Law: Entropy ..Clear precise notes