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?

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

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

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

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

For a gas, pressure p, volume v and temperature T are dependent on eac

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

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