The thermodynamic state of gas changes configuration from one with 3.8 *10¹⁸ microstates to one with 7.9 * 10¹⁹ microstates.The Boltzmann constant is 1.38 * 10^-23 J/K.The change in entropy is: A)"$\Delta$S = 0" B)"$\Delta$S = 1.05 * 10^-23 J/K" C)"$\Delta$S = -1.05 *10^-23 J/K" D)"$\Delta$S = 4.19 *10^-23 J/K" E)"$\Delta$S = -4.19*10^-23 J/K"

Question

Quizplus · Accepted Answer

The change in entropy ($\Delta S$) can be calculated using the formula $\Delta S = k \ln(\frac{W_f}{W_i})$, where $k$ is the Boltzmann constant, $W_f$ is the final number of microstates, and $W_i$ is the initial number of microstates. Substituting $k = 1.38 \times 10^{-23} \, J/K$, $W_f = 7.9 \times 10^{19}$, and $W_i = 3.8 \times 10^{18}$ into the formula gives a positive change in entropy, indicating an increase in disorder. The calculation results in $\Delta S = 4.19 \times 10^{-23} \, J/K$.

The Thermodynamic State of Gas Changes Configuration from One with 3.8