A certain amount of mono atomic gas undergoes a process for which ${\mathrm{U}}^{\mathrm{\beta }}\propto \mathrm{V}$ , where U is internal energy and V is volume of gas. It is found that the ratio $\frac{\mathrm{\Delta U}}{\mathrm{\Delta Q}}$ for the process is $\frac{1}{3}$ . What is the value of $\beta$