2. From statistical mechanics show that, \left(\frac{\partial \bar{E}}{\partial V}\right)_{\beta, N} + \beta \left(\frac{\partial p}{\partial \beta}\right)_{N, V} = -\bar{p}. From the thermodynamics we have \left(\frac{\partial E}{\partial V}\right)_{T, N} - T \left(\frac{\partial p}{\partial T}\right)_{N, V} = -p. Why can't \beta be linearly proportional to the temperature?
3. Show that for a particle confined to a cube of length a, the canonical ensemble average of the pressure is given by \bar{p} = \frac{2\bar{E}}{3V}.