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본문내용
D 는 이상기체식
P`V``=``R`T
와 연관하면
T_A``=``{P_A`V_A} over R```=```{P_A`V_D }over R
T_B``=``{P_B`V_B} over R```=```{P_B`V_C }over R
T_C``=``{P_C`V_C} over R```
T_D``=``{P_D`V_D} over R`
Thus
eta``=``1`-``V_C over V_D``{(``P_B``-``P_C``)} over {(``P_A``-``P_D``)}``=``1``-`` varupsilon `` LEFT ( {``P_B``-``P_C``} over {P_A``-``P_D} RIGHT )
reversible adiabatic process에서
P`V^ gamma ``=``rmconst
P_A`V_D`^gamma ``=``P_B`V_C`^ gamma```````````````````````````(``∵````V_D``=``V_A``,````V_C``=``V_B````)
P_C`V_C`^ gamma ``=``P_D`V_D`^ gamma
P_B over P_C``=``P_A over P_D```````````````````rm or````````````````P_C over P_D``=`` LEFT ( V_D over V_C RIGHT )^ gamma ``=`` LEFT ( 1 over varupsilon RIGHT ) ^ gamma
따라서 otto cycle의 효율은
eta``=`&`1``-`` varupsilon `{left( P_B over P_C``-``1 `right)} over {left( P_A over P_D``-``1``right)}`P_C over P_D``=``1``-`` varupsilon `P_C over P_D#```````````````````````&``(``∵```P_B over P_C``=``P_A over P_D``)#
eta``=``1``-`` varupsilon `left(``1 over varupsilon ``right)^gamma``=``1``-``left(`1 over varupsilon ^{gamma`-`1} right)
따라서 효율은 압축비에만 depand net shaft work는
W_S``=``eta`n`C_V`(`T_A`-`T_D`)``=``eta`n`R over{ gamma`-`1}`(`T_A``-``T_D`)
Actual otto cycle
P`V``=``R`T
와 연관하면
T_A``=``{P_A`V_A} over R```=```{P_A`V_D }over R
T_B``=``{P_B`V_B} over R```=```{P_B`V_C }over R
T_C``=``{P_C`V_C} over R```
T_D``=``{P_D`V_D} over R`
Thus
eta``=``1`-``V_C over V_D``{(``P_B``-``P_C``)} over {(``P_A``-``P_D``)}``=``1``-`` varupsilon `` LEFT ( {``P_B``-``P_C``} over {P_A``-``P_D} RIGHT )
reversible adiabatic process에서
P`V^ gamma ``=``rmconst
P_A`V_D`^gamma ``=``P_B`V_C`^ gamma```````````````````````````(``∵````V_D``=``V_A``,````V_C``=``V_B````)
P_C`V_C`^ gamma ``=``P_D`V_D`^ gamma
P_B over P_C``=``P_A over P_D```````````````````rm or````````````````P_C over P_D``=`` LEFT ( V_D over V_C RIGHT )^ gamma ``=`` LEFT ( 1 over varupsilon RIGHT ) ^ gamma
따라서 otto cycle의 효율은
eta``=`&`1``-`` varupsilon `{left( P_B over P_C``-``1 `right)} over {left( P_A over P_D``-``1``right)}`P_C over P_D``=``1``-`` varupsilon `P_C over P_D#```````````````````````&``(``∵```P_B over P_C``=``P_A over P_D``)#
eta``=``1``-`` varupsilon `left(``1 over varupsilon ``right)^gamma``=``1``-``left(`1 over varupsilon ^{gamma`-`1} right)
따라서 효율은 압축비에만 depand net shaft work는
W_S``=``eta`n`C_V`(`T_A`-`T_D`)``=``eta`n`R over{ gamma`-`1}`(`T_A``-``T_D`)
Actual otto cycle
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