黑体辐射公式的积分解及应用  

Integral Solution of the Formula of the Blackbody Radiation and its Application

作　　者：邓明德[1] 尹京苑[2] 刘西垣[3] 钱家栋[4] 房宗绯[1] 赵保宗[1] 酒全森[5] 

机构地区：[1]中国地震局综合观测中心,北京100039 [2]上海市地震局,上海200062 [3]北京大学数学科学院,北京100871 [4]中国地震局分析预报中心,北京100036 [5]首都师范大学数学系,北京100037

出　　处：《遥感信息》2002年第1期2-10,共9页Remote Sensing Information

基　　金：国家自然科学基金 (40 0 4 10 0 1);地震科学基金 (2 0 10 12 )资助

摘　　要：为了计算黑体在有界域 (λ1 - λ2 或 ν1 - ν2 )的辐射量 ,需对黑体辐射公式在有界域进行积分。本文对普朗克积分方程和瑞利 -金斯积分方程在有界域进行了求解 ,并给出了解析式。应用普朗克积分方程有界域 (λ1 - λ2 )的解 ,我们对不同岩性的岩石和土壤进行了不同物理温度实验 ,得出 :岩石和土壤等非黑体物质的辐射温度随波长的变化而变化 ,对于不同波长 ,辐射温度相差几度到十几度 ;在实验的试样中 ,绝大多数试样的辐射温度随波长变化出现了明显的 3个极大值和两个极小值 ,个别试样出现了明显的 4个极大值和 3个极小值 ;所有试样的辐射温度随波长变化的总趋势是随波长增大而减小 ;To calculate the radiation quantity of the blackbody in the bounded domain(λ 1-λ 2 or ν 1-ν 2),the integration of the formula of the blackbody radiation must be solved.In this paper, Planck's integral equation and Rayleigh Jeans' integral equation were solved in the bounded domain and the solution is given. Different physical temperature experiments of rock and soil with different lithologic characters have performed by applying the Planck's integral equation in the bounded domain (λ 1-λ 2). It has shown that the radiation temperature of the non-blackbody substance such as rock and soil varies with wavelength from several to more than ten degrees. The radiation temperature of the most samples has 3 obvious maximal and 2 minimal values. The radiation temperature of all samples shows a general tendency to get lower with the wavelength increase. However, the fact that the radiation temperature varies with wavelength does not change as physical temperature rises.

关 键 词：黑体辐射公式 积分解 岩石 土壤 辐射温度 瑞利-金斯公式 维恩公式 

分 类 号：P422[天文地球—大气科学及气象学] P407