Provide an Appropriate Response $\mathrm { L } = \frac { 1 } { \sqrt { 2 } \pi \mathrm { t } ^ { 2 } \mathrm { n } } \text {, }$

question 47

Multiple Choice

Provide an appropriate response.
-Under standard conditions, molecules of a gas collide billions of times per second. If each molecule has diameter average distance between collisions is given by
$\mathrm { L } = \frac { 1 } { \sqrt { 2 } \pi \mathrm { t } ^ { 2 } \mathrm { n } } \text {, }$ where $\mathrm { n }$ , the volume density of the gas, is a constant. Find $\frac { \mathrm { dL } } { \mathrm { dt } }$ .

• A) \(\frac { d L } { d t } = \frac { 2 } { \sqrt { 2 } \pi t ^ { 3 } n }\)
• B) \(\frac { \mathrm { dL } } { \mathrm { dt } } = \frac { 1 } { 2 \sqrt { 2 } \pi \mathrm { t } ^ { 3 } \mathrm { n } }\)
• C) \(\frac { \mathrm { dL } } { \mathrm { dt } } = - \frac { 2 } { \sqrt { 2 } \pi \mathrm { t } ^ { 3 } \mathrm { n } }\)
• D) \(\frac { \mathrm { dL } } { \mathrm { dt } } = - \frac { 1 } { \sqrt { 2 } \pi \mathrm { tn } }\)

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