Question

In which of the following processes involving ideal gas, entropy of the surrounding remains constant?

A. reversible isobaric heating
B. reversible adiabatic expansion
C. irreversible adiabatic compression
D. free expansion

Answer 1

To answer this question we should know what is entropy and about various thermodynamic processes. The disordeness or randomness is known as entropy. Entropy of the universe constitutes two parts, entropy of the system and entropy of the surrounding. The thermodynamic process which does not cause a surrounding has constant entropy.

Complete step by step answer: The process in which the smallest change occurs such that the system and surrounding come back to their original state is known as reversible process.

The process in which the change occurs such that the system and surrounding does not come back to their original state is known as an irreversible process.

The thermodynamic process in which no transfer of heat takes place is known as adiabatic process.

The thermodynamic process that occurs at constant pressure is known as an isobaric process.

The reversible heating at constant pressure is known as isobaric reversible isobaric heating. The thermodynamic processes occurring in open containers are considered as isobaric processes. Any change in the open system will affect the outer surrounding also, so entropy of the surrounding does not remain constant in reversible isobaric heating.

In reversible adiabatic expansion, the entropy change of the system is given by,

${\text{d}}{{\text{S}}_{{\text{system}}}}\,{\text{ = }}\,\dfrac{{{\text{dq}}}}{{\text{T}}}$

Similarly, the entropy change for surroundings also given by,

${\text{d}}{{\text{S}}_{{\text{surrounding}}}}\,{\text{ = }}\, - \dfrac{{{\text{dq}}}}{{\text{T}}}$

So, the total entropy of the universe is,

${\text{d}}{{\text{S}}_{{\text{universe}}}}\,{\text{ = }}\,\,{\text{d}}{{\text{S}}_{{\text{system}}}}\, + {\text{d}}{{\text{S}}_{{\text{surrounding}}}}$

${\text{d}}{{\text{S}}_{{\text{universe}}}}\,{\text{ = }}\,\,\,\dfrac{{{\text{dq}}}}{{\text{T}}}\, - \dfrac{{{\text{dq}}}}{{\text{T}}}$
${\text{d}}{{\text{S}}_{{\text{universe}}}}\,{\text{ = }}\,\,0$

In reversible processes heat is exchanged between two parts having the same temperature so, if entropy of one (system) increases, the entropy of another (surrounding) decreases. So, total change is zero. In reversible adiabatic expensing no heat is taken from the surrounding so, entropy of surrounding does not change. So, the entropy change in reversible adiabatic expansion remains constant.

In irreversible adiabatic compression, the phase and variable, pressure, volume and temperature all change so, entropy change of the system is calculated by following formulas:

${\text{dS}}\,{\text{ = }}\,\,\,{\text{n}}{{\text{C}}_{\text{v}}}{\text{ln}}\dfrac{{{{\text{T}}_{\text{2}}}}}{{{{\text{T}}_{\text{1}}}}}\,{\text{ + }}\,\,{\text{nRln}}\dfrac{{{{\text{V}}_{\text{2}}}}}{{{{\text{V}}_{\text{1}}}}}$
Or

${\text{dS}}\,{\text{ = }}\,\,\,{\text{n}}{{\text{C}}_{\text{p}}}{\text{ln}}\dfrac{{{{\text{T}}_{\text{2}}}}}{{{{\text{T}}_{\text{1}}}}}\,{\text{ + }}\,\,{\text{nRln}}\dfrac{{{{\text{P}}_1}}}{{{{\text{P}}_2}}}$
Or

${\text{dS}}\,{\text{ = }}\,\,\,\dfrac{{{\text{dq}}}}{{\text{T}}}$

Entropy of the surrounding universe in an irreversible process always increases.

For free expansion, the change in entropy of system depends upon the volume calculated by following formula:

${\text{dS}}\,{\text{ = }}\,\,{\text{nRln}}\dfrac{{{{\text{V}}_{\text{2}}}}}{{{{\text{V}}_{\text{1}}}}}$

Change in entropy of the surroundings is zero and entropy of the universe increases.

So, the entropy of surrounding remains constant in reversible adiabatic expansion.

Thus, the correct option is (B) $58.66{\text{ g}}$.

Note: Irreversible processes are spontaneous processes. Natural processes are spontaneous processes. In spontaneous processes entropy of the universe always increases. So, we can also say spontaneous changes are always irreversible. Free expansion is also an irreversible process. In a reversible process, change in total entropy remains zero. In adiabatic expansion, entropy of the system and surrounding remains constant.