เมื่ออัดแก๊สให้มีปริมาตรลดลง

��ʨ�ԧ �� ʷ��վĵԡ��ç�Ѻ��âͧ��ó�Ẻ ��㹸��ҵ��ͺ��͡�ҡ��ºҧ��Դ �վĵԡ��ʨ�ԧ ��ʷ��ԧ��ҵԡ��ҡ��ª�Դ ��ʺҧ��Դ��繻��ª��ժ��Ե �� ͡��ਹ��ʷ�� ǹ��ʤ��͹��͡䫴��ʷ��㹡�кǹ��ѧ��ʧ ��ਹ��ʷ��ૹ��ҡ��ش㹸��ҵ� �繵� ��ʺҧ��Դ��繾�ɵ�� ͹�͹͡䫴� ��ٴ��ҡ� �Ҩ�з��ª��Ե�� ҹ��ǹ��͡�ѡɳ�੾�е�Ƿ��ѵԷҧ��Ҿ��зҧ��

��ͧ�ҡ��բ�Ҵ��ҡ ��ö�дپĵԡ��ʷ��š��ͷ��е�� Ͷ�Ҩдٷ��ҹ� �е�� ѹ ��ҡ��ͧ��ŷ��ҡ �ѧ�� ֧�Դ�շ�ɮյ�ҧ� �ҡ��¢��ͷӹ�¾ĵԡ��ͧ��ʻ��ҳ�ҡ� �¾Ԩ�óҨҡ��ʷ��й�� š�� ҡ��ҧ��Ե��ʵ��зҧʶԵ��Ҥӹǳ��зӹ�¾ĵԡ��ʷ��Դ��鹷��

��ҹѡ��¹¡��͹�� (CO2) ˹ѡ 2 kg ��Կ��ջ��ҵ� 3 �١��ȡ�� ѧ��ԭ俿�ҴѺ�зѹ�ѹ��Կ��ҧ ��͹��Դ�͡�� ͡�ҡ�Կ�� س�� 27 ͧ�� ҹ��Դ��դ��ѹ��ʤ��͹��͡䫴��....?

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�ҡ�Ӷ��ҹ�� ѡ��¹�Ҩ��ª��Ե�ҡ��âҴ�͡��ਹ ��ҡ��Կ��ж١᷹��ʤ��͹��͡䫴��ҡ�� Դ��Դ �ѧ�� ѡ��¹��ùӹ��駻��ҳ�ҡ��ͧ��ԴʹԷ ��蹹�鹤��ʴط��͹��秷��դس��ѵԻ�ͧ�ѹ��Դ��

��ҷ�Һ�� ĵԡ��ͧ��ó�Ẻ ��Դ�� ԰ҹ�� š��ʶҹ��ç��зӵ�͡ѹ ��Ҩ��ç�֧�ٴ��ç��ѡ �͡�ҡ��ѧ��һ��ҵâͧ��š��դ�ҹ��ҡ��º�Ѻ��ҵâͧ�Ҫ�� վĵԡ��ó�Ẻ ��ʴ��ĵԡ��仵��ͧ��ش�� 仵��ٵ÷ҧ��Ե��ʵ��

��ʨ�ԧ�վĵԡ��͵��ͻ��͹�Ѻ�ٵ�

�� ö��㹷ء�� Ҥ��ѹ�٧�ҡ� ��š�Ţͧ��ʨ��Դ�ѹ�ҡ��֧�дѺ˹�觡��Դ�ç�֧�ٴ��ִ�˹��ǡѹ��ʡ��繢ͧ��㹷��ش ��觵��԰ҹ��š��ʶҹ��ç�ִ�˹��ҧ��š�� 繨�ԧ��š��ç�ִ�˹��ǵ�͡ѹ ��ʡ�ФǺ��繢ͧ�� 繵�

��ʨ�ԧ��ʴ��ĵԡ��仵��ͧ��ش��

��ҷӡ�÷��ͧ��ʨ�ԧ��Դ��ҧ� �ӹǹ��ҧ�� 1 �� ѹ

�ҡ�ٵ�

�� ӹǹ�� (n) ��ҡѺ 1 ��

��Ҩ��ѵ��ǹ��ҧ PV �Ѻ RT ��ҡѺ 1 ��Ͷ��ش�� Ҥ��ѹ��㴡�� ѵ��ǹ

��¡�� ῡ��Ѵ (compressibility factor =Z) �ͧ��

�Ԩ�óҡ�ҿ��ҧ

�� Z �Ѻ��ѹ P ��ҹ��ҧ

�ҡ��ҿ ��鹻��ʴ��ҿ�ͧ��ش�� ҿ��鹵ç��ѹ��ҡѺ 0 仵�ʹ�ء��ǧ��ѹ ��Ф�� Z = 1 �� ʨ�ԧ��оĵԵ��ó�Ẻ �ѧ�ʴ�㹡�ҿ

�ҡ��ҿ ��ʨ�ԧ 4 ��Դ�� ਹ(N2) ��ਹ(H2) ��෹(CH4) ��Ф��͹��͡䫴�(CO2) ��س�� 0 ͧ�� ҹ��оĵԵ��ش�� 鹡�ҿ��鹵ç��͹��鹻�� ҡ��÷��ͧ��ʷء��Դ��蹹�� ҡ��ҿ 㹪�ǧ��ѹ�� ( < 1atm) ��ҹ��դ�� Z ��§�Ѻ 1 ��蹤�ͼŤٳ�ͧ PV ��¹�ŧ�ҡ�ѡ ��ͤ��ѹ�٧�� Դ��§ູ�� ç�ִ�ٴ��ҧ��š��ö�Դ��š��ѹ�ҡ�� ѹ�٧� ��ʨ��դ��˹��٧��š��Դ�ѹ�ҡ�� ç��ҧ��š�Ũ֧�ռŵ�;ĵԡ��ͧ��ʨ�ԧ ��ҧ 1-200 atm ��ਹ�դ�� Z ��¡�� 1 ��ѧ�ҡ��鹨��դ�� Z �ҡ�� 1 �� ѹ�� ǹ��෹㹪�ǧ��ѹ 1-200 �� Z ��Ŵŧ ��Ǥ�� ҡ��˹�觷��ѹ��ҳ 400 atm ��Ф��͹��͡䫴� ��ѡɳФ��¡Ѻ��෹�� Z �ͧ��͹��͡䫴��Ŵŧ�ҡ��Ңͧ��෹ ��ʨ�ԧ�ء��Ǩ�� Z ��Ф�� Z �٧�� 1 ��ͤ��ѹ�٧�ҡ�� ѧ��ҿ��ҹ��

��Ѻ��ਹ ��෹ ��Ф��͹��͡䫴� ��ҿ㹪�ǧ��ѹ��ӡ�� 200 atm ��÷�� Z Ŵŧ �繼��Ҩҡ��ҵâͧ��Ŵŧ��ҧ�Ǵ�� ͤ��ѹ��㹪�ǧ�� Ţͧ��ҵ��ռ��ҡ��ҼŢͧ��ѹ ��ͻ��ҵ�Ŵŧ�֧��龨��

�դ��Ŵŧ��ӡ��˹�� Ͷ֧��˹�觻��ҵâͧ��öŴŧ��ա��ͧ�ҡ��Ѵ��鹷��ҧ��ͺ�� ҿ�� ѡɳС�ҿ�� 繼��Ҩҡ��ѹ��鹹��ͧ ��ͤ��ѹ��

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�ͧ�Ԩ�óҼŢͧ�س��Է��յ��ῡ��Ѵ�ͧ��ʴٺ�ҧ

��ҿ�ʴ��ѹ��ҧῡ��Ѵ�ͧ��ਹ��ͤ��ѹ��¹价��س��Ե�ҧ�

�ҡ��ҿ��¹�س��Ԣͧ��ਹ ��鹡�ҿ��ᵡ��ҧ�ѹ� ��س��٧��鹡�ҿ��§�Ѻ��鹡�ҿ�ͧ��ش��ҡ�� ա�ó�˹�觾Ԩ�óҡ�ҿ��ҹ��ҧ��ҿ �ʴ��ѹ��ҧ�Ťٳ��ѹ��л��ҵ�(PV) ��ͤ��ѹ(P) ��¹仢ͧ��ʹ��͹(Neon) �͡��ਹ(O2) ��Ф��͹��͡䫴�(CO2) ��ҧ�� 1 �� س�� 0 ͧ�� 273.15 K

��ҿ�ʴ� ��ѹ��ҧ�Ťٳ��ѹ�Ѻ��ҵ� (PV) �Ѻ ��ҵ� (V) �ͧ��ʹ��͹ �͡��ਹ �� ͹��͡䫴� �ӹǹ 1 ��ŷ��س�� 0 ͧ��

�ҡ��ҿ��ʨ�ԧ�վĵԡ��仵��ش�� ҿ��鹵ç��͹�Ѻ��鹻�Тͧ��ش�� ҡ��÷��ͧ��蹹�� Ԩ�ó��ʹ��͹��͡��ਹ��ѹ㹪�ǧ 0-0.1 atm ��Ҿĵԡ��ͧ��§�Ѻ��ش��鹡�ҿ��§�Ѻ��ҿ�ͧ��ش��(��鹻��) �ҡ��֡�Ҿ��ҧ�ͧ��š�Ţͧ�� й��դ�һ��ҳ 72 �ѧʵ�� š��ʨ֧��ú�ǹ��觡ѹ��Сѹ��ç��зӵ�͡ѹ�ҡ�ѡ ��ʹٷ��ѹ 1 atm ��ҿ�ͧ��ʷ��ҧ�͡�ҡ��鹡�ҿ�ش�� ʴ��ѹ��ա�Ժ�� (�ҡ 0.1 �� 1 atm) ��š��١�պ��Դ�ѹ�ҡ�� ѹ�֧�Դ��Ѻ��š�� ĵԡ�� й��Դ��ô֧�ٴ��С��ѡ�ѹ��ҧ��š��

�ҡ��ҿ��ҹ��о��ʨ�ԧ�վĵԡ��§�Ѻ��ش��Է��Ф��ѹ��ҡ� ��ͷ��ʹ��س��٧�ҡ� ��觡��˵ؼŷ�� ѹ��š��ҧ�ѹ�ҡ ��ǹ��س��٧�ҡ� ��ʡ��͹��Ǵ��ǵ��ѧ�ҹ�Ź�� ֧�Դ�ç�֧�ٴ��ç��ѡ��ҧ��š�Ź��ҡ��š��ҡ

�͡�˹�ͨҡ��дѧ�� ʨ�ԧ��仵��ͧ�� ѡ�Է��ʵ��ʧ�� Ҩ��ջѨ��ºҧ��ҧ��Ǣ�ͧ�Ѻ�ĵԡ��ʨ�ԧ��Դ��鹨�ԧ� ��Ф��ö�颺ǹ��÷ҧ��Ե��ʵ��͸Ժ�� Ŵ� ��㨧�� ҹ��

�ҹ��

Johannes Diderik van der Waals �.�. 1837 -1923

�ҹ�� ѡ��ԡ��ҡ��Ź��

��ö͸Ժ�¾ĵԡ��ͧ��բ�� ÷��ʹ͢��ҹ͡�ҡ��ҡ㹷ҧ��Ե��ʵ��ѧ ��ö�ӹ�¾ĵԡ��ա��

��ѹ�ͧ��ʷ��Դ��Դ�ҡ��š�Ţͧ��ʪ��Ѻ��ѧ�ͧ�Ҫ�е�ʹ�� Ԩ�ó��š�Ţͧ��ᴧ��ѧ��͹��Ҫ��ѧ�Ҫ�� ѧ�ٻ

��з��š��ᴧ�Ъ��ѧ�Ҫ�� ç�֧�ٴ�ҡ��š��Ǵ֧��š��ᴧ�� з��š��ᴧ��ѧ��ŧ �ŷ��ѹ��Դ�ҡ��š��ᴧ��ѧŴŧ��ӡ��ҡóբͧ��ê�Ẻ��١�֧�ҡ��š�� 觾ĵԡ��ͧ��ʨ�ԧ ��ͧ�Դ�ç�֧�ٴ��ҧ��š��蹹��ʹ�� 觼ŷ��ѹ��Դ��鹨�ԧ�դ�ҹ��ŧ

�ҹ��֧��ʹ� �� ѹ�ͧ��ó�Ẻ(

)�Ѻ��ѹ��Ѵ��ԧ(

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�� a �繤�Ҥ�� n �� V �繨ӹǹ��л��ҵâͧ�� ӴѺ

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��ù��¤�� ѹ��Ѵ��ԧ�ҡ��÷��ͧ(

) ��դ�ҹ��¡��Ҥ��ѹ�ͧ��ó�Ẻ(

) ��Һǡ��繤��ѹ��Ŵŧ�ҡ�ç�֧�ٴ��ҧ��š��к�

��к��ҵä�� ըӹǹ��š��(n) �ҡ��ʡ��Դ�ѹ�ҡ �ç�֧��ҧ��š�š��ҡ��¡��ѧ�ͧ ��һ��ҵ��鹡�з�� ç�֧�ٴ��ҧ��š��Ŵŧ��¡��ѧ�ͧ�蹡ѹ ��觻��ҵ��ҡ��š�š��ҧ�ѹ�ҡ�觼ŷ��ç�֧�ٴ��ҧ�ѹ��ŧ

�ա��ǹ˹��繡��ǡѺ��ҵâͧ��š��

��ҵ� V ��

��¶֧��ҵâͧ�Ҫ�� ֧��š�Ũ��բ�Ҵ��ҡ ��ͧ��ջ��ҵ��͹��˹�觴ѧ�ٻ

��š��ͧ��š��ѹ ��š�� r ˹�� ����š��ѡɳ��繷ç�� ҵâͧ��š�Ũ��ҡѺ

��ͧ�ҡ��ҾԨ�óһ��ҵ÷��š��˹�觡ѹ��ش�ٹ��ҧ�ͧ��š�� 2r (��鹻��ᴧ) ��觡��зҧ��ش�ٹ��ҧ�ͧ��š��չ��Թ��ö��š��ᴧ��ҡ��ش

��ամ�ѹ��ҡѺ 2r ˹�� ˹��š��ᴧ��ջ��ҵáѹ�� =

=

��蹤�ͻ��ҵáմ�ѹ�ͧ˹��š�� դ�� 8 ��Ңͧ��ҵ��ʨ�ԧ� ˹��š�� ж��ҹ� ��š�� С�� ҹ� ��Ңͧ˹��š��

��Ѻ N ��š�Ż��ҵ÷��մ�ѹ�� =

x N = nb

�ѧ�� ҵ÷��ӹǳ��

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�� n �繨ӹǹ��Ţͧ�� b �繤�Ҥ�� nb �֧��¶֧��ҵâͧ��š�� n �� ͼ�ҹ��

��С��

��ù��¡�� ��ÿҹ�� (van der waals equation)

��Ҥ�� a �� b ��Ѻ��Ъ�Դ��ҡѹ ��ҧ�� a �� b 㹵��ҧ

��ҧ�ʴ��Ҥ��ͧ�ҹ��ͧ��ʺҧ��Դ

�� a �͡��Һ�� š�Ţͧ��ʴ֧�ٴ�ѹ��§� �ҡ��ҧ�о�� (He) �դ�� a ��ӷ��ش �ʴ��š��ç�֧�ٴ��ش ��ǡѹ ��µ�� Ҩ��դ�� a ��͹�ѹ

�͡�ҡ�� ҡ��ҧ�о�� Ҵ��š��դ��ѹ��Ѻ�� b ��š��բ�Ҵ�˭� �� b ��դ��ҡ �� º��º��ҧ ��ਹ(H2) �Ѻ��ਹ(N2) �о��Ҥ�� b �ͧ��ਹ��š�ŷ��˭�� դ�� b ��ҡѺ 0.0391 ��ǹ�ͧ��ਹ �դ��ҡѺ 0.0266