※ 引述《TimJack (飽喀喀)》之銘言:
: http://i.imgur.com/o1hbYF0.jpg
: 請問大大這題如何表達溫度對時間函數
: 謝謝
這題應該是假設不同溫度的水會立即達熱平衡
否則根本沒法算
tank 1的溫度T_1 體積V_1
tank 2的溫度T_2 體積V_2
V_1(t) = V - (1/2)qt
V_2(t) = V + (1/2)qt
tank 1:
[V_1 - q dt] [dT_1] + (1/2) q dt [T_1 + dT_1 - T_2] = 0
=> V_1 [T_1]' + (1/2) q [T_1 - T_2] = 0 ----(1)
tank 2:
[V_2 - (1/2) q dt] [dT_2] + q dt [T_2 + dT_2 - T_1] = 0
=> V_2 [T_2]' + q [T_2 - T_1] = 0 ----(2)
(1)(2)微分方程
起始條件: T_1(0) = 20, T_2(0) = 70
=> V_1V_2[T_1]' + (1/2)V_2 q[T_1 - T_2] = 0
V_1V_2[T_2]' + V_1 q [T_2 - T_1] = 0
=> V_1V_2[T_1 - T_2]' + q[T_1 - T_2][(1/2)V_2 + V_1] = 0
initial condition T_1(0) - T_2(0) = -50
=> 可解出T_1 - T_2的時間函數F(t)
再把F(t)代入(1),(2)可解得T_1(t), T_2(t)
都是一階微分方程式
都可以解出來的
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 111.249.196.108
※ 文章網址: https://www.ptt.cc/bbs/Math/M.1431840554.A.BAC.html