For an ideal (perfect) gas, the change in entropy as a function of temperature and pressure is given by the general equation: $\Delta S = nC_p \ln\left(\frac{T_f}{T_i}\right) + nR \ln\left(\frac{p_i}{p_f}\right)$ For an isothermal process, the temperature remains constant ($T_i = T_f$), so $\ln\left(\frac{T_f}{T_i}\right) = \ln(1) = 0$. Substituting this into the equation, the first term becomes zero, and we are left with: $\Delta S = nR \ln\left(\frac{p_i}{p_f}\right)$.