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 \[\frac{{{\partial }^{3}}p}{\partial \,{{v}^{3}}}\,\,=\,\,0\]
Correct Answer: B
Solution :
At the critical point, \[\frac{\partial p}{\partial v}=0,\] \[\frac{{{\partial }^{2}}p}{\partial {{v}^{2}}}<0\]and \[\frac{{{\partial }^{3}}p}{\partial {{v}^{3}}}=0\] As the c.p. the value of \[p\,\,-\,\,v\] curve is maximum
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