Question

One mole of a perfect gas expands isothermally to ten times its original volume. The change in entropy is:
A. $1.0R$
B. $2.303R$
C. $10.0R$
D. $100.0R$

Answer 1

Hint:A perfect gas is the same as ideal gas. It obeys all the gas laws. When a gas expands its atoms tend to get more dispersed in the system thus increasing the volume of gas. We need to find the relation between the entropy and volume of a gas at isothermal conditions.
Formula used:
$\Delta S = 2.303nR\log \dfrac{{{V_f}}}{{{V_i}}}$
Where $\Delta S$ is the change in entropy, $n$ are the number of moles of gas, $R$ is the gas constant, ${V_f}$ is the final volume of the system, ${V_i}$ is the initial volume of the system.

Complete step by step answer:
Isothermal process is the process that occurs at constant temperature.
Entropy is the measure of disorder or randomness of molecules in a system. It is a thermodynamic quantity. It is denoted by $S$ . It is difficult to calculate the absolute entropy of the system. So we calculate the entropy during the change of state. The change in entropy from initial state to final state of a system is given as $\Delta S$ . Entropy is a state function since it depends on the initial and final state of the system. The entropy change of a system at isothermal reversible conditions is given by-
$\Delta S = \dfrac{{{q_{rev}}}}{T}$
Where ${q_{rev}}$ is the heat exchanged during the process and $T$ is the temperature.
The unit of entropy is $J{K^{ - 1}}$ or $cal{K^{ - 1}}$ .
The entropy change for an isothermal process when volume of system changes is given by-
$\Delta S = 2.303nR\log \dfrac{{{V_f}}}{{{V_i}}}$
Where $\Delta S$ is the change in entropy, $n$ are the number of moles of gas, $R$ is the gas constant, ${V_f}$ is the final volume of the system, ${V_i}$ is the initial volume of the system.
In the given problem,
Let the initial volume of the system be ${V_i}$ . The volume increases by ten times the initial volume then,
${V_f} = 10{V_i}$ , where ${V_f}$ is the final volume.
And, $n = 1$
Substituting the values,
$\
   \Rightarrow \Delta S = 2.303nR\log \dfrac{{{V_f}}}{{{V_i}}} \\
   \Rightarrow \Delta S = 2.303 \times 1 \times R \times \log \dfrac{{10{V_i}}}{{{V_i}}} \\
   \Rightarrow \Delta S = 2.303R\log 10 \\
   \Rightarrow \Delta S = 2.303R \\
\ $
The correct option is B.

Note:
-Entropy is a measure of disorder. When entropy increases the system is becoming more disordered from less disordered.
-The entropy for a cyclic process is zero.
-The entropy change in the equilibrium state is zero.