  Structural phase transitions in Pr$_{1-x}$La$_x$AlO$_3$ (0 $\leq x\leq$ 1)
single crystals have been studied through heat capacity and high-resolution
x-ray scattering measurements. For PrAlO$_3$, the heat capacity shows a sharp
first-order peak at the rhombohedral to orthorhombic transition, while a
classical mean-field anomaly is observed at the orthorhombic to monoclinic
transition at lower temperatures. The transition temperature and the heat
capacity anomaly of the two transitions diminish with increasing $x$, and only
a single rhombohedral to monoclinic transition is observed for $x = 0.8$.
Although this latter transition is required by group theory to be first order,
no such evidence is found in the heat capacity and x-ray scattering
measurements. Instead, the results are consistent with mean-field criticality,
with a small distribution of transition temperature originating from weak
disorder.
