Entropy Change - Practice Questions & MCQ

Mathematical Definition of Entropy

For a reversible isothermal process, Clausius defined it as the integral of all the terms involving heat exchange (q) divided by the absolute temperature T.

 

Here mol^-1 is also used as entropy being an extensive property depends upon the amount of the substance.

 

Entropy Changes in different processes:

1. Isothermal reversible process

 

2. Adiabatic reversible process

Note: Reversible adiabatic process is also called as Isentropic process

 

3. Isobaric process:

 

4. Isochoric process:

 

5. Entropy change in a process where both the Temperature as well as Volume or Pressure is changing

The above equation can also be written in terms of Pressure as 

Note: Remember the above general formula for the change in entropy.

 

6. Entropy change in irreversible processes:

Suppose a system at higher temperature T₁ and its surroundings is at lower temperature T₂.  'q' amount of heat goes irreversibly from the system to the surroundings.

So entropy increases in an irreversible process like conduction, radiation, etc.

 

7. Entropy changes during phase transition:

 

8. Entropy change when liquid is heated:

When a definite amount of liquid of mass 'm' and specific heat 's' is heated

Let us suppose a small amount of heat dq is added and as a result the temperature of the body increases by dT temperature

 

9. Entropy Change in Mixing of Ideal Gases:

Suppose n₁ mole of gas 'P' and n₂ mole of gas Q' are mixed; then total entropy change can be calculated as:

Here X₁ and X₂ are mole fractions of gases P and Q respectively.

 

It can be seen that the above expression is always positive for .