One mole of an ideal monoatomic gas expands isothermally and reversibly from an initial volume of to — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

For an isothermal expansion of any ideal gas, temperature is constant ($\Delta T = 0$), nullifying the $C_v$ term. Thus, $\Delta S_{sys} = nR \ln(\frac{V_2}{V_1}) = 2.303 nR \log(\frac{V_2}{V_1})$. Substituting parameters: $\Delta S_{sys} = 2.303 \times (1 \text{ mol}) \times (2 \text{ cal K}^{-1}\text{mol}^{-1}) \times \log(10) = 4.606 \times 1 = 4.606 \text{ cal K}^{-1}$.