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 (in thermal contact with the surroundings; 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.

Assuming $C{O}_2$ to be an ideal gas, ${\Delta }_{sys}S$ is:

• A. $27.4J{K}^{-1}$
• B. $9.1J{K}^{-1}$
• C. $-27.4J{K}^{-1}$
• D. $-9.1J{K}^{-1}$

Answer 1

The correct option is A $27.4J{K}^{-1}$

As we know,

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 ${\Delta }_{sys}S=\frac{3\times 8.314\times 288.15\times ln\frac{30}{10}}{288.15}$

$=27.4J{K}^{-1}$