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

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Chemistry Hải Đăng 5 years 2021-07-31T05:19:52+00:00 2021-07-31T05:19:52+00:00 1 Answers 50 views 0

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

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nguyetanh · Answer 1 · 2021-07-31T05:20:56+00:00

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 $_{AB}$ [tex]=nC_{v}(T_{f}-T_{i} )[/tex]

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

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

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

$Q_{CD}=-ve and Q_{DA}=-ve$ 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 $=\frac{2}{13}$

$=0.15$