Question

one gram molecule of an ideal gas at S.T.P is subjected to a reversible adiabatic expansion to double its volume. find the change in internal energy in the process . given cp/cv =1.4

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{\gamma }=1.4 \\ {\mathrm{T}}_1{{\mathrm{V}}_1}^{\mathrm{\gamma }-1}={\mathrm{T}}_2{{\mathrm{V}}_2}^{\mathrm{\gamma }-1} \\ {\mathrm{T}}_2=\frac{{\mathrm{T}}_1{{\mathrm{V}}_1}^{\mathrm{\gamma }-1}}{{{\mathrm{V}}_2}^{\mathrm{\gamma }-1}}=\frac{273}{{\left(2\right)}^{1.4-1}}=207\mathrm{K} \\ \mathrm{Change}\mathrm{in}\mathrm{internal}\mathrm{energy}, \\ ∆\mathrm{U}=\frac{\mathrm{R}}{\mathrm{\gamma }-1}\left({\mathrm{T}}_1-{\mathrm{T}}_2\right) \\ ∆\mathrm{U}=\frac{8.31\left(273-207\right)}{1.4-1}=1369.5\mathrm{J} \end{gathered}$$