Numerical problems 65 p3.16 the joule coefficient is defined by (at/av)y (1/cv)[p t(ap/at)y]. calculate the joule coefficient for an ideal gas and for a van der waals gas. p3.17 using the result of equation (3.8), (ap/at)v-β/k express β as a function of k and v, n for an ideal gas, and β as a function of b, k, and v, for a van der waals gas p3.18 show that the expression (aujav)r keal gas and for aandeai h t(p/at)- p can be written in the form au p3.19 derive an expression for the internal pressure of a gas that obeys the bethelot equation of state, rt p3.20 because u is a state function, (a/av (au/at)v)r aar (au/av)r)v. using this relationship, show that cv/av)t 0 for an ideal gas. starting with the van der waals equation of state, fino n expression for the total differential dp in terms of dv and t. by calculating the mixed partial derivatives