1.

The mathematical conditions at the critical point for a pure substance would be:

A. \[\frac{\partial p}{\partial v}<0\,;\,\,\frac{{{\partial }^{2}}p}{\partial {{v}^{2}}}=0\] and \[\frac{{{\partial }^{3}}p}{\partial {{v}^{3}}}=0\]
B. \[\frac{\partial p}{\partial v}=0\,;\,\,\frac{{{\partial }^{2}}p}{\partial {{v}^{2}}}<0\] and \[\frac{{{\partial }^{3}}p}{\partial {{v}^{3}}}=0\]
C. \[\frac{\partial p}{\partial v}=0\,;\,\,\frac{{{\partial }^{2}}p}{\partial {{v}^{2}}}=0\] and \[\frac{{{\partial }^{3}}p}{\partial {{v}^{3}}}<0\]
D. \[\frac{\partial p}{\partial v}=0\,;\,\,\frac{{{\partial }^{2}}p}{\partial {{v}^{2}}}=0\] and \[\frac{{{\partial }^{3}}p}{\partial \,{{v}^{3}}}\,\,=\,\,0\]
Answer» C. \[\frac{\partial p}{\partial v}=0\,;\,\,\frac{{{\partial }^{2}}p}{\partial {{v}^{2}}}=0\] and \[\frac{{{\partial }^{3}}p}{\partial {{v}^{3}}}<0\]


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