Solve the Problem $\mathrm { P } ( \mathrm { V }$

question 391

Multiple Choice

Solve the problem.
-The Van der Waals equation provides an approximate model for the behavior of real gases. The equation is $\mathrm { P } ( \mathrm { V }$ , $\mathrm { T } ) = \frac { \mathrm { RT } } { \mathrm { V } - \mathrm { b } } - \frac { \mathrm { a } } { \mathrm { V } ^ { 2 } }$ , where $\mathrm { P }$ is pressure, $\mathrm { V }$ is volume, $\mathrm { T }$ is Kelvin temperature, and $\mathrm { a } , \mathrm { b }$ , and $\mathrm { R }$ are constants. Find the partial derivative of the function with respect to each variable.

• A) \(P _ { V } = - \frac { 2 a } { V ^ { 3 } } + \frac { R T } { ( V - b ) ^ { 2 } } ; P _ { T } = \frac { R } { V - b }\)
• B) \(\mathrm { PV } _ { \mathrm { V } } = \frac { \mathrm { R } } { \mathrm { V } - \mathrm { b } } ; \mathrm { P } _ { \mathrm { T } } = \frac { 2 \mathrm { a } } { \mathrm { V } ^ { 3 } } - \frac { \mathrm { RT } } { ( \mathrm { V } - \mathrm { b } ) ^ { 2 } }\)
• C) \(\mathrm { PV } _ { \mathrm { V } } = \frac { 2 \mathrm { a } } { \mathrm { V } } - \frac { \mathrm { RT } } { ( \mathrm { V } - \mathrm { b } ) ^ { 2 } } ; \mathrm { P } _ { \mathrm { T } } = \frac { \mathrm { R } } { \mathrm { V } - \mathrm { b } }\)
• D) \(\mathrm { PV } _ { \mathrm { V } } = \frac { 2 \mathrm { a } } { \mathrm { V } ^ { 3 } } - \frac { \mathrm { RT } } { ( \mathrm { V } - \mathrm { b } ) ^ { 2 } } ; \mathrm { P } _ { \mathrm { T } } = \frac { \mathrm { R } } { \mathrm { V } - \mathrm { b } }\)

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