Question

What is the thermal efficiency of an engine that takes n moles of diatomic ideal gas through the cycle

Answer 1

Answer:

The thermal efficiency of an engine is $0.15$ that is 15%

Explanation:

Specific heat of a gas at constant volume is

$C_{v}=\frac{fR}{2}$

here, $f=$degree of freedom

$R=$universal gas constant

Thermal efficiency of a cycle is

$\frac{total workdone}{gross heat absorbed}$

Gross heat absorbed is amount of heat that absorbed.

ω$=P_{o} V_{o}$

$Q_{AB}=$Δ$V_{AB}+$ω$_{AB}$$=nC_{v}(T_{f}-T_{i} )$

       $=n\frac{f}{2}(RT_{f}-RT_{i} )$$=\frac{f}{2}(P_{o}V_{o} )$

$Q_{BC}=n(\frac{f}{2}+1 )R(T_{f}-T_{i} )$

       $=(\frac{f}{2} +1)(4P_{o}V_{o}-2P_{o}V_{o} )$=$=(\frac{f}{2}+1)2P_{o}V_{o}$

$Q_{CD}=-ve and Q_{DA}=-ve$    these 2 are not the part of gross heat

η$=\frac{P_{o}V_{o} }{(\frac{3f}{2}+2 )(P_{o}V_{o})}$

  $=\frac{1}{(\frac{3f}{2}+2 )}$

For monoatomic gas $f=3$

η$=\frac{2}{13}$

  $=0.15$