question_answer

         For a gas, pressure p, volume v and temperature T are dependent on each other. Then which one of the following \[p\,-\,v\,-T\] relationships will be obeyed? 

A) \[{{\left( \frac{\partial p}{\partial T} \right)}_{v}}\,{{\left( \frac{\partial v}{\partial T} \right)}_{p}}\,{{\left( \frac{\partial v}{\partial p} \right)}_{T}}\,=-\,\,1\]

B) \[{{\left( \frac{\partial p}{\partial T} \right)}_{v}}\,{{\left( \frac{\partial T}{\partial v} \right)}_{p}}\,{{\left( \frac{\partial v}{\partial p} \right)}_{T}}=-\,\,1\]

C) \[{{\left( \frac{\partial p}{\partial T} \right)}_{v}}\,{{\left( \frac{\partial v}{\partial T} \right)}_{p}}\,{{\left( \frac{\partial p}{\partial v} \right)}_{T}}=-\,\,1\]

D) \[{{\left( \frac{\partial p}{\partial T} \right)}_{v}}={{\left( \frac{\partial T}{\partial v} \right)}_{p}}\,{{\left( \frac{\partial p}{\partial v} \right)}_{T}}\]