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) \(\frac { \mathrm { dL } } { \mathrm { dt } } = - \frac { 1 } { \sqrt { 2 } \pi \mathrm { tn } }\)

---

Definitions:

Public Good

An item or service made available to all societal members at no cost, regardless of profit, by either governmental bodies or private individuals or groups.

Common Good

A concept referring to either policies or infrastructure that benefit all members of a community or society.

External Good

Often misinterpreted; should likely be "external good," relating to positive externalities, benefits received by those not directly involved in a transaction.

Nonrival-in-consumption

A property of a good whereby one person's consumption does not diminish the utility of that good for others.