结构推理 Figure 8.11suggests that in a typical atmosphere, about one-third of the surface area of the particles is contained in particles with diameter centered about 0.02, about one-third in particles with diameter centered about 0.3, and about one-third in particles with diameter centered about 10. If the true situation were that the distribution by air was exactly one-third in each of these diameter ranges and if, instead of the board distributions shown in Fig 8.11, all of the particles were exactly either 0.02, 0.3 or 10in diameter, then (a) What would the fraction by weight be for each of the three particles sizes? (b) What would the fraction by number be for each of the three particles sizes?

【正确答案】解：因为这三种直径的颗粒物按面积分布相等，所以设其数量分别为S1，S2，S3。重量分别为m1，m2，m3。球的表面积为，则 S1：S2：S3=（D2D3）2：（D1D3）2：（D1D2）2=9：0.04：0.000036 因此各颗粒物的数量分布为：0.02颗粒物占99.56/%，0.3颗粒物占0.44/%，10颗粒物0.0036/%。同理： m1：m2：m3==D1：D2：D3=0.02：0.3：10 因此各颗粒物按重量分布为：0.02颗粒物占0.20/%，0.3颗粒物占2.91/%，10颗粒物96.89/%。

【答案解析】