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

Identify the critical decision areas of operations management.

Gain insight into trends and challenges in achieving productivity growth.

Comprehend the scope of operations management activities including planning, organizing, leading, and controlling.

Understand the principle of hidden production functions in various sectors.

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