Question

12£®Ò»¶¨ÖÊÁ¿µÄÀíÏëÆøÌå±»»îÈû·â±ÕÔÚÆø¸×ÄÚ£¬»îÈûÖÊÁ¿Îªm¡¢ºá½ØÃæ»ýΪS£¬¿ÉÑØÆø¸×±ÚÎÞĦ²Á»¬¶¯²¢±£³ÖÁ¼ºÃµÄÆøÃÜÐÔ£¬Õû¸ö×°ÖÃÓëÍâ½ç¾øÈÈ£¬³õʼʱ·â±ÕÆøÌåµÄζÈΪT₁£¬»îÈû¾àÀëÆø¸×µ×²¿µÄ¸ß¶ÈΪH£¬´óÆøѹǿΪP_o£®ÏÖÓÃÒ»µçÈÈË¿¶ÔÆøÌ建Âý¼ÓÈÈ£¬Èô´Ë¹ý³ÌÖеçÈÈË¿´«µÝ¸øÆøÌåµÄÈÈÁ¿ÎªQ£¬»îÈûÉÏÉýµÄ¸ß¶ÈΪ$\frac{H}{4}$£¬Çó£º
¢ñ£®´ËʱÆøÌåµÄζȣ»
¢ò£®ÆøÌåÄÚÄܵÄÔö¼ÓÁ¿£®

Answer 1

·ÖÎö ¢ñ£®ÆøÌå·¢ÉúµÈˆR‰ä»¯£¬ÓɸÇ-ÂÀÈø¿Ë¶¨ÂÉ¿ÉÒÔÇó³öζȣ»
¢ò£®ÓÉÈÈÁ¦Ñ§µÚÒ»¶¨ÂÉ¿ÉÒÔÇó³öÔö¼ÓµÄÄÚÄÜ

½â´ð ½â£º¢ñ£®ÆøÌå¼ÓÈÈ»ºÂýÉÏÉý¹ý³ÌÖУ¬´¦ÓÚµÈѹ¹ý³Ì£¬ÉèÉÏÉý$\frac{H}{4}$ʱζÈΪ${T}_{2}^{\;}$£¬Ôò
   ${V}_{1}^{\;}=SH$            ¢Ù
 ${V}_{2}^{\;}=S£¨H+\frac{H}{4}£©$                   ¢Ú
   $\frac{{V}_{1}^{\;}}{{T}_{1}^{\;}}=\frac{{V}_{2}^{\;}}{{T}_{2}^{\;}}$                        ¢Û
µÃ${T}_{2}^{\;}=\frac{5}{4}{T}_{1}^{\;}$¢Ü
¢ò£®ÉÏÉý¹ý³ÌÖУ¬¾ÝÈÈÁ¦Ñ§µÚÒ»¶¨Âɵãº
¡÷U=Q+W                  ¢Ý
ʽÖУº$W=-£¨{p}_{0}^{\;}S+mg£©\frac{H}{4}$        ¢Þ
Òò´Ë£º$¡÷U=Q-£¨{p}_{0}^{\;}S+mg£©\frac{H}{4}$       ¢ß
´ð£º¢ñ£®´ËʱÆøÌåµÄζÈ$\frac{5}{4}{T}_{1}^{\;}$£»
¢ò£®ÆøÌåÄÚÄܵÄÔö¼ÓÁ¿$Q-£¨{p}_{0}^{\;}S+mg£©\frac{H}{4}$

µãÆÀ ±¾Ì⿼²éÁËÇóζȡ¢ÄÚÄܵÄÔöÁ¿£¬·ÖÎöÇå³þÆøÌå״̬±ä»¯¹ý³Ì£¬Ó¦ÓøÇ-ÂÊÈø¿Ë¶¨ÂÉ¡¢ÈÈÁ¦Ñ§µÚÒ»¶¨Âɼ´¿ÉÕýÈ·½âÌ⣮