Solve the Problem , Where $\mathrm { P }$ Is Pressure $\mathrm { V }$

question 341

Multiple Choice

Solve the problem.
-The Redlich-Kwong equation provides an approximate model for the behavior of real gases. The equation is $\mathrm { P } ( \mathrm { V } , \mathrm { T } ) = \frac { \mathrm { RT } } { \mathrm { V } - \mathrm { b } } - \frac { \mathrm { a } } { \mathrm { T } ^ { 1 / 2 } \mathrm {~V} ( \mathrm {~V} + \mathrm { b } ) }$ , where $\mathrm { P }$ is pressure, $\mathrm { V }$ is volume, $\mathrm { T }$ is Kelvin temperature, and $a , b$ , and $\mathrm { R }$ are constants. Find the partial derivative of the function with respect to each variable.

• A) \(\mathrm { PV } _ { \mathrm { V } } = \frac { \mathrm { a } ( 2 \mathrm {~V} + \mathrm { b } ) } { \mathrm { V } ^ { 2 } ( \mathrm {~V} + \mathrm { b } ) ^ { 2 } \mathrm {~T} ^ { 1 / 2 } } + \frac { \mathrm { RT } } { ( \mathrm { V } - \mathrm { b } ) ^ { 2 } } ; \mathrm { P } _ { \mathrm { T } } = - \frac { \mathrm { a } } { 2 \mathrm {~T} ^ { 3 / 2 } \mathrm {~V} ( \mathrm {~V} + \mathrm { b } ) } + \frac { \mathrm { R } } { \mathrm { V } - \mathrm { b } }\)
• B) \(\mathrm { PV } _ { \mathrm { V } } = \frac { \mathrm { a } ( 2 \mathrm {~V} + \mathrm { b } ) } { \mathrm { V } ^ { 2 } ( \mathrm {~V} + \mathrm { b } ) ^ { 2 } \mathrm {~T} ^ { 1 / 2 } } - \frac { \mathrm { RT } } { ( \mathrm { V } - \mathrm { b } ) ^ { 2 } } ; \mathrm { P } _ { \mathrm { T } } = \frac { \mathrm { a } } { 2 \mathrm {~T} ^ { 3 / 2 } \mathrm {~V} ( \mathrm {~V} + \mathrm { b } ) } + \frac { \mathrm { R } } { \mathrm { V } - \mathrm { b } }\)
• C) \(\mathrm { PV } _ { \mathrm { V } } = \frac { \mathrm { a } ( 2 \mathrm {~V} + \mathrm { b } ) } { 2 \mathrm {~V} ^ { 2 } ( \mathrm {~V} + \mathrm { b } ) ^ { 2 } \mathrm {~T} ^ { 1 / 2 } } - \frac { \mathrm { RT } } { ( \mathrm { V } - \mathrm { b } ) ^ { 2 } } ; \mathrm { P } _ { \mathrm { T } } = \frac { \mathrm { a } } { \mathrm { T } ^ { 3 / 2 } \mathrm {~V} ( \mathrm {~V} + \mathrm { b } ) } + \frac { \mathrm { R } } { \mathrm { V } - \mathrm { b } }\)
• D) \(\mathrm { PV } _ { \mathrm { V } } = \frac { \mathrm { a } ( 2 \mathrm {~V} + \mathrm { b } ) } { \mathrm { V } ^ { 2 } ( \mathrm {~V} + \mathrm { b } ) ^ { 2 } \mathrm {~T} ^ { 1 / 2 } } + \frac { \mathrm { RT } } { ( \mathrm { V } - \mathrm { b } ) ^ { 2 } } ; \mathrm { P } _ { \mathrm { T } } = \frac { \mathrm { a } } { 2 \mathrm {~T} ^ { 3 / 2 } \mathrm {~V} ( \mathrm {~V} + \mathrm { b } ) } - \frac { \mathrm { R } } { \mathrm { V } - \mathrm { b } }\)

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