Question
Question: One mole of a perfect gas expands isothermally to ten times its original volume. The change in entro...
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
Solution
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:
ΔS=2.303nRlogViVf
Where ΔS is the change in entropy, n are the number of moles of gas, R is the gas constant, Vf is the final volume of the system, Vi 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 ΔS . 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-
ΔS=Tqrev
Where qrev is the heat exchanged during the process and T is the temperature.
The unit of entropy is JK−1 or calK−1 .
The entropy change for an isothermal process when volume of system changes is given by-
ΔS=2.303nRlogViVf
Where ΔS is the change in entropy, n are the number of moles of gas, R is the gas constant, Vf is the final volume of the system, Vi is the initial volume of the system.
In the given problem,
Let the initial volume of the system be Vi . The volume increases by ten times the initial volume then,
Vf=10Vi , where Vf is the final volume.
And, n=1
Substituting the values,
⇒ΔS=2.303nRlogViVf ⇒ΔS=2.303×1×R×logVi10Vi ⇒ΔS=2.303Rlog10 ⇒ΔS=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.