Question

The second law of Thermodynamics is a fundamental law of science. In this problem, we consider the Thermodynamics of an ideal gas, phase transition and chemical equilibrium.
Three moles of $C{O}_2$ gas expands isothermally $(inthermalcontactwiththesurroundings;temperature={15.0}^{\circ }C)$ against a fixed external pressure of $1.00bar$. The initial and final volumes of the gas are $10.0L$ and $30.0L$, respectively. Change in entropy of the universe is:

• A. $34.34J{K}^{-1}$
• B. $-34.34J{K}^{-1}$
• C. $20.46J{K}^{-1}$
• D. $-20.46J{K}^{-1}$

Answer 1

The correct option is C $20.46J{K}^{-1}$

work done $=q=nRTln\frac{V_2}{V_1}$
$=3\times 8.314\times 288.15\times ln\left(\begin{array}{c}\frac{30}{10}\end{array}\right)$
$\therefore$ $\Delta S=\frac{q}{T}$
or ${\Delta }_{sys}S=\frac{3\times 8.314\times 288.15\times ln\frac{30}{10}}{288.15}$
$=27.4J{K}^{-1}$
And
${\Delta }_{surr}S=6.94J/K$
${\Delta }_{uni}S={\Delta }_{surr}S+{\Delta }_{sys}S$

$=6.94J/K+27.4$

$=20.46J/K$