Solve the Problem $$\mathrm { e } = \frac { \mathrm { Q } _ { \mathrm { h } } - \mathrm { Q } _ { \mathrm { C } } } { \mathrm { Q } _ { \mathrm { h } } } \text {, }$$

question 286

Multiple Choice

Solve the problem.
-A heat engine is a device that converts thermal energy into other forms. The thermal efficiency, e, of a heat engin defined by
$$\mathrm { e } = \frac { \mathrm { Q } _ { \mathrm { h } } - \mathrm { Q } _ { \mathrm { C } } } { \mathrm { Q } _ { \mathrm { h } } } \text {, }$$
where $\mathrm { Q } _ { h }$ is the heat absorbed in one cycle and $\mathrm { Q } _ { \mathrm { C } }$ , the heat released into a reservoir in one cycle, is a constant. Find $\frac { d ^ { 2 } e } { d h ^ { 2 } }$

• A) \(\frac { \mathrm { d } ^ { 2 } \mathrm { e } } { \mathrm { dQ } _ { \mathrm { h } ^ { 2 } } } = \frac { \mathrm { Q } _ { \mathrm { C } } } { \mathrm { Q } _ { \mathrm { h } ^ { 2 } } }\)
• B) \(\frac { d ^ { 2 } e } { d Q _ { h } ^ { 2 } } = \frac { - 2 Q _ { C } } { Q _ { h } { } ^ { 3 } }\)
• C) \(\frac { d ^ { 2 } e } { d _ { h ^ { 2 } } ^ { 2 } } = \frac { Q _ { c } } { Q _ { h ^ { 3 } } }\)
• D) \(\frac { \mathrm { d } ^ { 2 } \mathrm { e } } { \mathrm { dQ } _ { \mathrm { h } } ^ { 2 } } = \frac { - \mathrm { Q } _ { \mathrm { C } } } { 2 \mathrm { Qh } ^ { 2 } }\)

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Definitions:

Adaptive Value

The extent to which a trait or behavior positively affects an organism's survival and reproductive success in its environment.

Cognitive

Related to mental processes such as thinking, knowing, remembering, and problem-solving, determining how we understand and interact with the world.

Ethnographic

pertains to the qualitative research method focused on the systematic study of cultures and communities through direct observation and participation.

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An instinctive response to perceived threats or dangers, often for survival purposes.