Provide an Appropriate Response $e = \frac { Q _ { h } - Q _ { c } } { Q _ { h } }$

Multiple Choice

Provide an appropriate response.
-A heat engine is a device that converts thermal energy into other forms. The thermal efficiency, e, of a heat engin defined by
$e = \frac { Q _ { h } - Q _ { c } } { Q _ { h } }$ where $\mathrm { Q } _ { \mathrm { h } }$ 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 $\frac { \mathrm { d } ^ { 2 } \mathrm { e } } { \mathrm { dQ } ^ { 2 } }$ .

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