Question

If one mole of monatomic ideal gas expanded from $2$ atm to $0.5$ atm at $27^\circ C$, then the entropy change will be
A) R ln Z
B) 4R ln Z
C) 3R ln Z
D) 2R ln Z

Answer 1

Hint: We need to discuss the change in entropy: the ratio of heat transfer to temperature QT. We must remember that the second law of thermodynamics states in terms of entropy: the total entropy of a system either increases or remains constant; it never decreases.

Complete answer:
We have to know that the entropy, the measure of a system's thermal energy per unit temperature, is unavailable for doing useful work. Because work is obtained from ordered molecular motion, the amount of entropy is also a measure of the molecular disorder, or randomness, of a system.
$\Delta S = nR\ln \left( {\dfrac{{{P_1}}}{{{P_2}}}} \right)$
Here symbols have their usual meaning
Now we can substitute the known values we get,
$\Delta S = 1 \times 8.314 \times 2.303 \times \log \dfrac{2}{{0.5}}$
$\Delta S = 1 \times 8.314 \times 2.303 \times \log 4$
Substituting the value of log we get,
$ \Rightarrow \Delta S = 1 \times 8.314 \times 2.303 \times 0.6$
On multiplication we get,
$ \Rightarrow \Delta S = 11.488J{K^{ - 1}}$
This is a complete solution even if it is not asked in the question but from this also we can infer from this solution that the answer for this question is ΔS = n R ln Z .
A heat reservoir is a constant temperature heat source or sink. Because the temperature is uniform, there is no heat transfer across a finite temperature difference and the heat exchange is reversible. From the definition of entropy,
\[\Delta S = \dfrac{Q}{T}\]

Note:
We need to know that the second law puts restriction on useful conversion of q to w. It follows from observation of directionality to natural or spontaneous process. It provides a set of principles for determining the direction of spontaneous change and also for determining equilibrium state of a system.