Question

To increase the thermal efficiency of a reversible power cycle operating between thermal reservoirs at TH and Tc, would you increase TH while keeping To constant, or decrease To while keeping TH constant? Are there any natural limits on the increase in thermal efficiency that might be achieved by such means? Consider how η responds to a change in temperature-if either temperature is changed by some r, which will have a greater effect? Hint: Check the derivative of η with regard to TH and Tc separately

Answer 1

$\ T_{c}$ has greater effect.

Explanation:

$\eta_{\max }=1-\frac{T_{c}}{T_{A}}$

$T_{c}$ = Temperature of cold reservoir

$T_{H}$ = Temperature of hot reservoir

when $T_{c}$ is decreased by 't',

$\eta_{\text {incre }}$ = $1-\frac{\left(\tau_{c}-t\right)}{T_{H}}$

$=n \ + \frac{t}{T_{n}}$      $-(i)$

when ${T_{H}}$ is increased by 'T'

$\eta_{i n c}=\frac{n+\frac{t}{T_{H}}}{\left(1+\frac{k}{T_{H}}\right)}-(ii)$

$\eta_{\text {incre }} \ T_{c}>\eta_{\text {incre }} T_{\text {H }}$