Question

For a reversible spontaneous change, the entropy change is:
A. \[\dfrac{{{\rm{\Delta E}}}}{{\rm{T}}}\]
​B. \[\dfrac{{{\rm{P\Delta V}}}}{{\rm{T}}}\]
​C. \[\dfrac{{\rm{q}}}{{\rm{T}}}\]
​D. RT (log K)

Answer 1

Hint: The statement of the second law of thermodynamics is "the entropy of the universe increases for an irreversible process". Entropy stays constant for a reversible process.

Complete Step by Step Solution:
Entropy is the measure of the extent of disorderness in a thermodynamic system.
It indicates the irregularity or deficiency of the ordered structure in a thermodynamic system.
This is symbolized by ‘S’.
It is an extensive property as the value of entropy or entropy change relies on the quantity of matter present in a thermodynamic system.
Entropy is a state function as its value does not depend on the path by which the system has attained a specific state.
It depends on only the initial and final state of the system.
For a reversible spontaneous reaction i.e., for an infinitesimally small change,
\[{\rm{dS = }}\dfrac{{{\rm{d}}{{\rm{q}}_{{\rm{rev}}}}}}{{\rm{T}}}\]
where
dS=small change in entropy
\[{\rm{d}}{{\rm{q}}_{{\rm{rev}}}}\] =small change in the quantity of heat exchanged in a process carried out reversibly at a constant temperature T.
The change in entropy,
 \[\Delta {\rm{S = }}\int {\dfrac{{{\rm{d}}{{\rm{q}}_{{\rm{rev}}}}}}{{\rm{T}}}} \]
So, \[\Delta {\rm{S = }}\dfrac{{{{\rm{q}}_{{\rm{rev}}}}}}{{\rm{T}}}\]

So, option C is correct.

Note: Since entropy is a state function, the change of entropy for a change of state from one state to another will be the same whether the change is reversible or not. Entropy is expressed by a unit of heat divided by the unit of absolute temperature. It is expressed in terms of joules per degree Kelvin or J/K. This is known as the entropy unit, e.u. .