One mole of Helium is placed in a container at a pressure of 2atm and at a temperature of 300 K. The gas expand irreversibly and adiabatically to a pressure of 1 atm. The $\Delta S$ of system is (Cal/K)___
Given:  $(C_p=\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.R,R=2cal{k}^{-1})$, log2 = 0.3, log5 = 0.7

$$\begin{gathered} \Delta U=n{C}_V\Delta T\Delta U=-P_{\epsilon \times t}\left(\Delta V\right) \\ \frac{\Delta T}{\Delta V}=\frac{-p_{\epsilon \times t}}{n{C}_v}=-\frac{2}{3R} \\ nR{T}_2/P_2=V_2=R{T}_2 \\ \raisebox{1ex}{$nR{T}_1$}\!\left/ \!\raisebox{-1ex}{$P_1$}\right.=V_1=\frac{1\times R\times 300}{2}=150R \\ \frac{T_2-T_1}{V_2-V_1}=\frac{T_2-300}{R(T_2-150)}=-\frac{2}{3R} \\ 3T_2-900=-2T_2+300 \\ 5T_2=1200\Rightarrow T_2=240K \end{gathered}$$

$\Delta S= 2.3n{C}_{p}log\frac{T_2}{T_1}+2.3nR\log \frac{P_1}{P_2}$

$=2.3\times 1\times \frac{5}{2}\times 2\log \frac{240}{300}+2.3\times 1\times 2\log 2 = 0.23 Cal$