termo

March 17, 2019 | Author: Carlos Matías Olmedo Valencia | Category: Refrigeration, Quantity, Phases Of Matter, Physics, Física y matemáticas
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c                       c            !    "    !  #  $  "    %& '()"  '   & ()    ë     

ܲ௘ ൌ ͳ͸Ͳሾܾܽ‫ݎ‬ሿܲ௦ ൌ ʹሾܾܽ‫ݎ‬ሿ ܶ௘ ൌ ͷ͸Ͳሾ‰ܿ ሿ‫ܣ‬௦ ൌ ͳͲͲͲሾܿ݉ଶ ሿ ൌ Ͳǡͳሾ݉ଶ ሿ ݉ ܸ௘ ൌ ͺͲ ቂ ቃ ‫ݏ‬ ௞௚ ௞௚ ݉ሶ ൌ ͳͲͲͲ ቂ ቃ ൌ ͳ͸ǡ͸͹ ቂ ቃ



௠௜௡

 ܲ௘ ܶ௘  ‫ݒ‬௘ ൌ ͲǡͲʹͳ͹ʹ ቂ

௠య ௞௚

ቃ



 ܲ௦ ǡ     ‫ݒ‬௦ ൌ Ͳǡͺͺͷ͹ ቂ



௠య ௞௚

ቃ

݉ሶ ൌ

‫ܣ‬௘ ‫ܸ כ‬௘  ‫ݒ‬௘

݉ሶ ൌ

‫ܣ‬௦ ‫ܸ כ‬௦  ‫ݒ‬௦

݉ ‫ܣ‬௘ ‫ כ‬ͺͲ ቂ ቃ ݇݃ ‫ ܣ  ֜  ݏ‬ൌ Ͷǡͷ͵ ‫ିͲͳ כ‬ଷ ሾ݉ଶ ሿ ൌ Ͷͷǡ͵ሾܿ݉ଶ ሿ ͳ͸ǡ͸͹ ൤ ൨ൌ ௘ ݉ଷ ‫݃݁ݏ‬ ͲǡͲʹͳ͹ʹ ൤ ൨ ݇݃  

݉ Ͳǡͳሾ݉ଶ ሿ ‫ܸ כ‬௦ ݇݃ ൨ൌ  ֜  ܸ௦ ൌ ͳͶ͹ǡ͸ͷ ቂ ቃ ͳ͸ǡ͸͹ ൤ ଷ ݉ ‫ݏ‬ ‫݃݁ݏ‬ Ͳǡͺͺͷ͹ ൤ ൨ ݇݃    

c *     c         &         "       &    "      &c + '()$ " %,&()     ë     

ܲ௘ ൌ ͸Ͳሾܾܽ‫ݎ‬ሿܲ௦ ൌ Ͳǡ͸ሾܾܽ‫ݎ‬ሿ ܶ௘ ൌ ͷͲͲሾ‰‫ ܥ‬ሿ݀௦ ൌ Ͷǡͷሾ݉ሿ ݉ ܸ௘ ൌ ͳͲͲ ቂ ቃ ‫ݏ‬ ሾ ݀௘ ൌ Ͳǡ͸ ݉ሿ  ܲ௘ ܶ௘  ‫ݒ‬௘ ൌ ͲǡͲͷ͸͸ͷ ቂ

௠య ௞௚

ቃ

 ܲ௦ ǡ     ‫ݒ‬௦ ൌ ʹǡ͹͵ʹ ቂ 



      

௠య ௞௚

ቃ

݉ ߨ ଶ ଶ ‫ܣ‬௦ ‫ܸ כ‬௦ Ͷ ‫ כ‬ሺͲǡ͸ሻ ሾ݉ ሿ ‫ ͲͲͳ כ‬ቂ ‫ ݏ‬ቃ ݇݃ ݇݃ ݉ሶ ൌ ൌ ൌ Ͷͻͻǡͳ ൤ ൨ ൌ ͳǤ͹ͻ͸Ǥ͹͸Ͳ ൤ ൨ ଷ ݉ ‫ݒ‬௦ ‫ݏ‬ ݄ ͲǡͲͷ͸͸ͷ ൤ ൨ ݇݃ ߨ ‫ כ‬ሺͶǡͷሻଶ ሾ݉ଶ ሿ ‫ܸ כ‬௘ ݇݃ Ͷ  Ͷͻͻǡͳ ൤ ൨ ൌ ݉ଷ ݄ ʹǡ͹͵ʹ ൤ ൨ ݇݃ ݉ ֜ ܸ௘ ൌ ͺͷǡ͹͵ ቂ ቃ ‫ݏ‬

c          &-

.'       !    /  & !  0   !1       c & /&2! + '() /  &()    %   ë 

݉ ܸ௘ ൌ ʹͲ ቂ ቃܲ௦ ൌ ͳǡͺሾܾܽ‫ݎ‬ሿ ‫ݏ‬ ݉ ܶ௘ ൌ ʹ͹ሾ‰‫ ܥ‬ሿܸ௦ ൌ ͷͲ ቂ ቃ ‫ݏ‬ ‫ܣ‬௘ ൌ ͲǡͲͲͺሾ݉ଶ ሿ‫ܣ‬௦ ൌ ͲǡͲͲ͵ሾ݉ଶ ሿ

݉ሶ ൌ ͳͺ ቂ

௄௚

௠௜௡

ቃ ൌ Ͳǡ͵ ቂ ቃ ௄௚ ௦

ëë     ܲ௘ ‫ܣ כ‬௘ ‫ܸ כ‬௘ ൌ 

݉ሶ ‫ܶ כ ܴ כ‬௘  ܲ‫ܯ‬

‫݃ܭ‬ Ͳǡ͵ ቂ ‫ ݏ‬ቃ ݉ ܾܽ‫݉ כ ݎ‬ଷ ଶ ቉ ‫ͲͲ͵ כ‬ሾι‫ܭ‬ሿ ܲ௘ ‫Ͳ כ‬ǡͲͲͺሾ݉ ሿ ‫ Ͳʹ כ‬ቂ ቃ  ൌ  ‫Ͳ כ‬ǡͲͺ͵ͳͶ ቈ ݇݃ ‫ݏ‬ ‫ܭ‰ כ ݈݋݉݃ܭ‬ ͵ʹ ൤‫݈݋݉݃ܭ‬൨ ֜ ܲ௘ ൌ ͳǡͶ͸ሾܾܽ‫ݎ‬ሿ

ëë    ܲ௦ ‫ܣ כ‬௦ ‫ܸ כ‬௦ ൌ 

ͳǡͺሾܾܽ‫ݎ‬ሿ ‫Ͳ כ‬ǡͲͲ͵ሾ݉

ଶሿ

݉ሶ ‫ܶ כ ܴ כ‬௦  ܲ‫ܯ‬

‫݃ܭ‬ Ͳǡ͵ ቂ ‫ ݏ‬ቃ ݉ ܾܽ‫݉ כ ݎ‬ଷ ቉ ‫ܶ כ‬௦  ‫ כ‬ͷͲ ቂ ቃ  ൌ  ‫Ͳ כ‬ǡͲͺ͵ͳͶ ቈ ݇݃ ‫ݏ‬ ‫݈݋݉݃ܭ‬ ‫כ‬ ‰‫ܭ‬ ͵ʹ ൤‫݈݋݉݃ܭ‬൨ ֜ ܶ௦ ൌ ͵Ͷ͸ǡͶሾι‫ܭ‬ሿ

   

c *                   &  3& 1c     /       & !                  ! 435   "   /    &! 6()$ " &()      ë 

ܲ௘ ൌ ͳͲͲሾ‫ܽ݅ݏ݌‬ሿܲ௦ ൌ ͺͲሾ‫ܽ݅ݏ݌‬ሿ ܶ௘ ൌ ͺͲሾ‰‫ ܨ‬ሿ ൌ ͷͶͲሾ‰ܴሿܶ௦ ൌ ͳʹͲሾ‰‫ܨ‬ሿ ൌ ͷͺͲሾ‰ܴሿ ‫ܣ‬௘ ൌ ͸ሾ݅݊ଶ ሿ ൌ ͲǡͲͶʹሾ݂‫ ݐ‬ଶ ሿ‫ܣ‬௦ ൌ Ͷሾ݅݊ଶ ሿ ൌ ͲǡͲʹͺሾ݂‫ ݐ‬ଶ ሿÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ

ܸ௘ ൌ ͳ͹ͷ ቂ

௙௧

௦௘௚

ቃÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ

ëë     ܲ௘ ‫ܣ כ‬௘ ‫ܸ כ‬௘ ൌ 

ͳͲͲሾ‫ܽ݅ݏ݌‬ሿ ‫Ͳ כ‬ǡͲͶʹሾ݂‫ ݐ‬ଶ ሿ ‫ͳ כ‬͹ͷ ൤

݉ሶ ‫ܶ כ ܴ כ‬௘  ܲ‫ܯ‬

݂‫ݐ‬ ‫ ݐ݂ כ ܽ݅ݏ݌‬ଷ ݉ሶ ቉ ‫ כ‬ͷͶͲሾ‰ܴሿ ൨ൌ ‫Ͳͳ כ‬ǡ͹͵ ቈ ݈ܾ݉ ‫݃݁ݏ‬ ݈ܾ݉‫݈݋‬ ‫כ‬ ‰ܴ ቃ ʹͺǡͻ͹ ቂ ݈ܾ݉‫݈݋‬ ֜ ݉ሶ ൌ ͵ǡ͸͹ ൤

ëë    ܲ௦ ‫ܣ כ‬௦ ‫ܸ כ‬௦ ൌ 

݈ܾ݉ ൨ ‫݃݁ݏ‬

݉ሶ ‫ܶ כ ܴ כ‬௦  ܲ‫ܯ‬

݈ܾ݉ ൨ ‫ ݐ݂ כ ܽ݅ݏ݌‬ଷ ‫݃݁ݏ‬ ଶ ቉ ‫ כ‬ͷͺͲሾ‰ܴሿ ‫Ͳͳ כ‬ǡ͹͵ ቈ ͺͲሾ‫ܽ݅ݏ݌‬ሿ ‫Ͳ כ‬ǡͲʹͺሾ݂‫ ݐ‬ሿ ‫ܸ כ‬௦  ൌ  ݈ܾ݉ ݈ܾ݉‫ܴ‰ כ ݈݋‬ ቃ ʹͺǡͻ͹ ቂ ݈ܾ݉‫݈݋‬ ͵ǡ͸͹ ൤

݂‫ݐ‬ ൨ ֜ ܸ௦ ൌ ͵ͷͳǡͻ͸ ൤ ‫݃݁ݏ‬

    

c !1  7 $      & 2          &*        !              "    "          1           + ' ()  $  "   %& ()      &()  &   ௠ ௠ ‫׊‬ሶൌ Ͳǡͳ ቂ ቃ ൌ ͲǡͲͲͳ͹ ቂ௦௘௚ቃ య



ெ௜௡



௘௜௧௘

‫ݒכ‬

௚௨

ൌ ௘௟

௧௜௩

֜



௘௜௧௘

଴ǡଽ

೘య ଵǡ଴଴ଵ଼‫כ‬ଵ଴షయ ൤ ൨ ಼೒

ൌ ͺͻͺǡ͵ͺ ቂ

௄௚

௠య

ቃ

ë 

ܶ௘ ൌ ʹͲሾ‰‫ ܥ‬ሿܶ௘ ൌ ܶ௦ ൌ ʹͲሾ‰‫ܥ‬ሿ  ՜  ௘ ൌ ௦  ݀௘ ൌ ͳͲሾܿ݉ሿ݀௦ ൌ ͹ሾܿ݉ሿ ݉ሶ ൌ  ‫׊‬ሶ ‫ כ‬

௘௜௧௘

݉ሶ ൌ ‫ܣ‬௘ ‫ܸ כ‬௘ ‫ כ‬

݉ሶ ൌ ‫ܣ‬௦ ‫ܸ כ‬௦ ‫ כ‬

       

ൌ ͲǡͲͲͳ͹ ቂ ௘௜௧௘

௘௜௧௘

௠య

௦௘௚

ቃ ‫ כ‬ͺͻͺǡ͵ͺ ቂ

֜ ͳǡͷ͵ ቂ

௄௚

௦௘௚

֜ ͳǡͷ͵ ቂ

௄௚

௠య

ቃ ൌ ͳǡͷ͵ ቂ

௄௚

ቃ

ቃ ൌ ‫ כ‬ሺͲǡͳଶ ሻሾ݉ଶ ሿ ‫ܸ כ‬௘ ‫ כ‬ͺͻͺǡ͵ͺ ቂ ସ గ

֜ ܸ௘ ൌ Ͳǡʹʹ ൤

௦௘௚

௄௚

௦௘௚

݉ ൨ ‫݃݁ݏ‬

௄௚

௠య

ቃ ൌ ‫ כ‬ሺͲǡͲ͹ଶ ሻሾ݉ଶ ሿ ‫ܸ כ‬௦ ‫ כ‬ͺͻͺǡ͵ͺ ቂ గ ସ

֜ ܸ௦ ൌ ͲǡͶͶ ൤

݉ ൨ ‫݃݁ݏ‬

ቃ

௄௚

௠య

ቃ

c 2     22!c    c2c    $  "     %,  +              $  "  & 6 ()    '%8%&()    & ()"  '     ë 

ܲ௘ ൌ ͵Ͳሾܾܽ‫ݎ‬ሿܲ௦ ൌ Ͷͺሾܾܽ‫ݎ‬ሿ ܶ௘ ൌ ͵ʹͲሾԨሿܶ௦ ൌǫ

ܸ௘ ൌ Ͳܸ௦ ൌ ͷ͵ͷ ቂ ݉ሶ ൌ ͺǤͲͲͲ ൤

‫݃ܭ‬ ‫݃ܭ‬ ൨ ൌ ʹǡʹʹ ൤ ൨ ݄ ‫݃݁ݏ‬

 ܲ௘ ܶ௘  ݄௘ ൌ ͵ǤͲͶ͵ǡͶ ቂ ቃ ௄௃

௄௚

 

ܳ െ ܹ ൌ ο݄ ൅ ο‫ ܿܧ‬൅ ο‫݃݌ܧ‬



՜ ο݄ ൅ ο‫ ܿܧ‬ൌ Ͳ

ͳ ሺͷ͵ͷଶ െ Ͳሻ ‫ܬܭ‬ ‫ܬܭ‬ ൤ ൨ ൌ Ͳ ൬݄௦ െ ͵ǤͲͶ͵ǡͶ ൤ ൨൰ ൅ ʹ ͳǤͲͲͲ ‫݃ܭ‬ ‫݃ܭ‬ ‫ܬܭ‬ ֜ ݄௦ ൌ ʹǤͻͲͲǡ͵ ൤ ൨ ‫݃ܭ‬

 ܲ௦ ݄௦  ܶ௦ ൌ ʹͶͲǡͶሾԨሿ

 ‫ݒ‬௦ ൌ ͲǡͳͶͺͶ ቂ

௠య ௄௚

ቃ

݉ሶ ൌ

‫ܣ‬௦ ‫ܸ כ‬௦  ‫ݒ‬௦

݉ ‫ܣ‬௦ ‫ כ‬ͷ͵ͷ ቂ ቃ ݇݃ ‫ ܣ  ֜  ݏ‬ൌ ͸ǡͳ͸ ‫ିͲͳ כ‬ସ ሾ݉ଶ ሿ ൌ ͸ǡͳ͸ሾܿ݉ଶ ሿ ʹǡʹʹ ൤ ൨ൌ ௦ ݉ଷ ‫݃݁ݏ‬ ͲǡͳͶͺͶ ൤ ൨ ݇݃    



௦௘௚

ቃÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ

c 2*               3       !       &1c     $  "     ,  +              $  "  & 6 ()    '     9 & ()         3,, &()"    

‫݈ܽ݀݅ܽܵܽ݀ܽݎݐ݊ܧ‬ ܲ௘ ൌ ͶͲͲሾ‫ܽ݅ݏ݌‬ሿܲ௦ ൌ ʹͲͲሾ‫ܽ݅ݏ݌‬ሿ

ܶ௘ ൌ ͸ͲͲሾԬሿܸ௦ ൌ ͳǡͶ͹ͷ ൤

ܸ௘ ൌ Ͳ ݉ሶ ൌ ͳͺǤͲͲͲ ൤

 ܲ௘ ܶ௘  ݄௘ ൌ ͳǤ͵Ͳ͸ǡ͸ ቂ

݈ܾ݉ ݈ܾ݉ ൨ ൌ ͷ൤ ൨ ݄‫ݎ‬ ‫݃݁ݏ‬

஻௧௨

௟௕௠

 



ቃ

ܳ െ ܹ ൌ ο݄ ൅ ο‫ ܿܧ‬൅ ο‫݃݌ܧ‬

‫ݑݐܤ‬ ͳ ݂‫ ݐ‬ଶ ቉‫כ‬ ֜ ൬݄௦ െ ͳǤ͵Ͳ͸ǡ͸ ൤ ൨൰ ൅ ‫ͳ כ‬ǡͶ͹ͷଶ ቈ ݈ܾ݉ ʹ ‫݃݁ݏ‬ଶ

ሾ‫ݑݐܤ‬ሿ ൌ Ͳ ݈ܾ݉ ‫ ݐ݂ כ‬ଶ ʹͷǤͲ͵͸ǡͷ ൤ ൨ ‫݃݁ݏ‬ଶ

‫ݑݐܤ‬ ൨ ֜ ݄௦ ൌ ͳǤ͵Ͳ͸ǡ͸ ൤ ݈ܾ݉

 ܲ௦ ݄௦  ܶ௦ ൌ ͷͻͳǡ͵ሾԬሿ‫ݒ‬௦ ൌ ͵ǡͲʹͻ ቂ 

 

௙௧ య

௟௕௠

ቃ

݂‫ݐ‬ ‫ܣ‬௦ ‫ͳ כ‬ǡͶ͹ͷ ൤‫݃݁ݏ‬൨ ݈ܾ݉ ‫ܣ‬௦ ‫ܸ כ‬௦ ֜ ͷ൤ ൨ൌ  ݉ሶ ൌ ݂‫ ݐ‬ଷ ‫݃݁ݏ‬ ‫ݒ‬௦ ൨ ͵ǡͲʹͻ ൤ ݈ܾ݉ ֜ ‫ܣ‬௦ ൌ ͳͲǡʹ͹ሾ݂‫ ݐ‬ଶ ሿ



݂‫ݐ‬ ൨ ‫݃݁ݏ‬

c c      "       2:  &   !           "     & !           !&   c   + ' ()  $  "   %& ()    '    %8%& ()          &()" '    

‫݈ܽ݀݅ܽܵܽ݀ܽݎݐ݊ܧ‬ ܲ௘ ൌ ͳǡͺሾܾܽ‫ݎ‬ሿܲ௦ ൌ ʹሾܾܽ‫ݎ‬ሿ

ܶ௘ ൌ ʹͲሾԨሿܸ௦ ൌ ͷͲ ൤

ܸ௘ ൌ ͳͶͲ ൤

݉ ൨ ‫݃݁ݏ‬

݉ ൨ ‫݃݁ݏ‬

‫ܣ‬௘ ൌ ͳͲͲሾܿ݉ଶ ሿ ൌ ͲǡͲͲͳሾ݉ଶ ሿ  ܲ௘ ܶ௘  ‫ݒ‬௘ ൌ Ͳǡͳʹ͹ʹ͵ ቂ

ቃ݄௘ ൌ ʹ͸ͺǡʹ͵ ቂ ቃ ௞௚

௠య

௄௃

௄௚

݉ ൨ ͲǡͲͲͳሾ݉ଶ ሿ ‫ͳ כ‬ͶͲ ൤ ‫ܣ‬௘ ‫ܸ כ‬௘ ‫݃ܭ‬ ‫݃݁ݏ‬ ݉ሶ ൌ ൌ ൌ ͳǡͳ ൤ ൨ ଷ ݉ ‫ݒ‬௘ ‫݃݁ݏ‬ Ͳǡͳʹ͹ʹ͵ ൤ ൨ ݇݃





ܳ െ ܹ ൌ ο݄ ൅ ο‫ ܿܧ‬൅ ο‫݃݌ܧ‬

‫ܬܭ‬ ͳ ሺͷͲଶ െ ͳͶͲଶ ሻ ‫ܬܭ‬ ֜ ൬݄௦ െ ʹ͸ͺǡʹ͵ ൤ ൨൰ ൅ ‫כ‬ ൤ ൨ ൌ Ͳ ‫݃ܭ‬ ʹ ͳǤͲͲͲ ‫݃ܭ‬ ‫ܬܭ‬ ֜ ݄௦ ൌ ʹ͹͸ǡ͹ͺ ൤ ൨ ‫݃ܭ‬

 ܲ௦ ܶ௦  ܶ௦ ൌ ͵ͲሾԨሿ‫ݒ‬௦ ൌ Ͳǡͳͳͺͷ͸ ቂ 

௠య ௞௚

ቃ

݉ ൨ ‫ܣ‬௦ ‫ כ‬ͷͲ ൤ ‫ܣ‬௦ ‫ܸ כ‬௦ ‫݃ܭ‬ ‫݃݁ݏ‬ ݉ሶ ൌ  ֜ ͳǡͳ ൤ ൨ൌ  ݉ଷ ‫ݒ‬௦ ‫݃݁ݏ‬ Ͳǡͳͳͺͷ͸ ൤ ൨ ݇݃ ֜ ‫ܣ‬௦ ൌ ͲǡͲͲʹ͸ሾ݉ଶ ሿ ൌ ʹ͸ሾܿ݉ଶ ሿ

 

c c!   /     c1&;c2         /  &c! !  0      "&*2! 6()         % & ()  $  "   %&  ()  /     ‫݈ܽ݀݅ܽܵܽ݀ܽݎݐ݊ܧ‬ ܲ௘ ൌ ͷ͹ሾܾ݉ܽ‫ݎ‬ሿܸ௦ ൌ ͳͺ ൤

݉ ൨ ‫݃݁ݏ‬

ܶ௘ ൌ െͷ͵ሾԨሿ ൌ ʹʹͲሾι‫ܭ‬ሿ‫ܣ‬௦ ൌ Ͳǡͻ͵ሾ݉ଶ ሿ

ܸ௘ ൌ ͺͺͲ ൤

݉ ൨ ‫݃݁ݏ‬

‫ܣ‬௘ ൌ Ͳǡͷʹሾ݉ଶ ሿ

  ܶ௘  ݄௘ ൌ ʹͳͻǡͻ͹ ቂ ቃ ௄௃

௄௚

 

ܳ െ ܹ ൌ ο݄ ൅ ο‫ ܿܧ‬൅ ο‫݃݌ܧ‬

‫ܬܭ‬ ͳ ሺͳͺଶ െ ͺͺͲଶ ሻ ‫ܬܭ‬ ֜ ൬݄௦ െ ʹͳͻǡͻ͹ ൤ ൨൰ ൅ ‫כ‬ ൤ ൨ ൌ Ͳ ‫݃ܭ‬ ʹ ͳǤͲͲͲ ‫݃ܭ‬

 ݄௦  ܶ௦ ൌ ͸ͲͲሾι‫ܭ‬ሿ

‫ܬܭ‬ ֜ ݄௦ ൌ ͸Ͳ͹ǡͲͳ ൤ ൨ ‫݃ܭ‬

 ëë    ܲ௘ ‫ܣ כ‬௘ ‫ܸ כ‬௘ ൌ ֜ ͲǡͲͷ͹ሾܾܽ‫ݎ‬ሿ ‫Ͳ כ‬ǡͷʹሾ݉ଶ ሿ ‫ כ‬ͺͺͲ ቂ



௦௘௚

ቃൌ

௠ሶ

௉ெ

‫ܶ כ ܴ כ‬௘  ௠ሶ

಼೒ ቃ ଶ଼ǡଽ଻ቂ ಼೒೘೚೗

֜ ݉ሶ ൌ Ͷͳǡ͵ͳ ൤ 

‫Ͳ כ‬ǡͲͺ͵ͳͶ ቂ

‫݃ܭ‬ ൨ ‫݃݁ݏ‬

௕ ‫כ‬௠ య

௄௚௠௢௟‫כ‬ι௄

ቃ ‫Ͳʹʹ כ‬ሾι‫ܭ‬ሿ

ëë   ܲ௦ ‫ܣ כ‬௦ ‫ܸ כ‬௦ ൌ ֜ ܲ௦ ‫Ͳ כ‬ǡͻ͵ሾ݉

                    

ଶሿ

‫ͳ כ‬ͺ ቂ



௦௘௚

ቃൌ

௠ሶ

௉ெ

‫ܶ כ ܴ כ‬௦ 

಼೒ ቃ ೞ೐೒ ಼೒ ଶ଼ǡଽ଻ቂ ቃ ಼೒೘೚೗

ସଵǡଷଵቂ

‫Ͳ כ‬ǡͲͺ͵ͳͶ ቂ

֜ ܲ௦ ൌ Ͷǡʹͷሾܾܽ‫ݎ‬ሿ

௕ ‫כ‬௠ య

௄௚௠௢௟‫כ‬ι௄

ቃ ‫ כ‬͸ͲͲሾι‫ܭ‬ሿ

c c                & 1 %  !   0         & c %  !!   #  c %8%         "     &* !  + ' ()  /  '    %8%& ()      -   &  ()  /  "               ‫݈ܽ݀݅ܽܵܽ݀ܽݎݐ݊ܧ‬ ܲ௘ ൌ ͸ሾܾܽ‫ݎ‬ሿܲ௦ ൌ ͳሾܾܽ‫ݎ‬ሿ

ܶ௘ ൌ ͹ͶͲሾι‫ܭ‬ሿܶ௦ ൌ ͶͷͲሾι‫ܭ‬ሿ

ܸ௘ ൌ ͳʹͲ ൤

݉ ݉ ൨ܸ௦ ൌ ʹʹͲ ൤ ൨ ‫݃݁ݏ‬ ‫݃݁ݏ‬

‫ܣ‬௘ ൌ Ͷǡͻͳሾܿ݉ଶ ሿ ൌ Ͷǡͻͳ ‫ିͲͳ כ‬ସ ሾ݉ଶ ሿ

 ܶ௘  ݄௘ ൌ ͹ͷ͸ǡͶͶ ቂ ቃ ௄௃

 ൌ െͳͷ ൤

‫ܬܭ‬ ൨ ‫݃ܭ‬

௄௚

 ܶ௦  ݄௦ ൌ Ͷͷͳǡͺ ቂ ቃ ௄௃

ο‫ ܿܧ‬ൌ ‫כ‬ ଵ ଶ

ቂ ቃ ൌ ͳ͹ ቂ ቃ

൫ଶଶ଴మ ିଵଶ଴మ ൯ ௄௃ ଵǤ଴଴଴

௄௚

௄௚

௄௃

௄௚

ëë    ܲ௘ ‫ܣ כ‬௘ ‫ܸ כ‬௘ ൌ ֜ ͸ሾܾܽ‫ݎ‬ሿ ‫ כ‬Ͷǡͻͳ ‫ିͲͳ כ‬ସ ሾ݉ଶ ሿ ‫ Ͳʹͳ כ‬ቂ



௦௘௚

௠ሶ

௉ெ

ቃൌ

‫ܶ כ ܴ כ‬௘ 

಼೒ ଶ଼ǡଽ଻ቂ ቃ ಼೒೘೚೗

֜ ݉ሶ ൌ Ͳǡͳ͹ ൤ 

֜ െͳͷ ൤



௠ሶ

‫݃ܭ‬ ൨ ‫݃݁ݏ‬

‫Ͳ כ‬ǡͲͺ͵ͳͶ ቂ

ܳሶ െ ܹሶ ൌ ݉ሶሺο݄ ൅ ο‫ ܿܧ‬൅ ο‫݃݌ܧ‬ሻ

௕ ‫כ‬௠ య

௄௚௠௢௟‫כ‬ι௄

ቃ ‫ כ‬͹ͶͲሾι‫ܭ‬ሿ

‫ܬܭ‬ ‫݃ܭ‬ ‫݃ܭ‬ ‫ܬܭ‬ ‫ܬܭ‬ ‫ܬܭ‬ ൨ ‫Ͳ כ‬ǡͳ͹ ൤ ൨ െ  ܹሶ ൌ Ͳǡͳ͹ ൤ ൨ ൜൬Ͷͷͳǡͺ ൤ ൨ െ ͹ͷ͸ǡͶͶ ൤ ൨൰ ൅ ͳ͹ ൤ ൨ൠ ‫݃ܭ‬ ‫݃݁ݏ‬ ‫݃݁ݏ‬ ‫݃ܭ‬ ‫݃ܭ‬ ‫݃ܭ‬ ֜ ܹሶ ൌ Ͷ͸ǡ͸ͺሾ‫ ܹܭ‬ሿ

ëë   ܲ௦ ‫ܣ כ‬௦ ‫ܸ כ‬௦ ൌ ֜ ͳሾܾܽ‫ݎ‬ሿ ‫ܣ כ‬௦ ‫ Ͳʹʹ כ‬ቂ



௦௘௚

ቃൌ

௠ሶ

௉ெ

‫ܶ כ ܴ כ‬௦ 

಼೒ ቃ ೞ೐೒ ಼೒ ଶ଼ǡଽ଻ቂ ቃ ಼೒೘೚೗

଴ǡଵ଻ቂ

‫Ͳ כ‬ǡͲͺ͵ͳͶ ቂ

௕ ‫כ‬௠ య

௄௚௠௢௟‫כ‬ι௄

֜ ‫ܣ‬௦ ൌ ͻǡͻͺ ‫ିͲͳ כ‬ସ ሾ݉ଶ ሿ ൌ ͻǡͻͺሾܿ݉ଶ ሿ

ʹ ‫ כ‬Ͷǡͻͳሾܿ݉ଶ ሿ ʹ ‫ܣ כ‬௘ ൌඨ ൌ ͳǡ͹ͺሾܿ݉ሿ ՜ ݀௘ ൌ ඨ ߨ ߨ ʹ ‫ܣ כ‬௦ ʹ ‫ͻ כ‬ǡͻͺሾܿ݉ଶ ሿ ඨ ඨ ՜ ݀௦ ൌ ൌ ൌ ʹǡͷʹሾܿ݉ሿ ߨ ߨ ֜

             

݀௘ ͳǡ͹ͺሾܿ݉ሿ ൌ ൌ Ͳǡ͹ ݀௦ ʹǡͷʹሾܿ݉ሿ

ቃ ‫ כ‬ͶͷͲሾι‫ܭ‬ሿ

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