超易f.3phy有關thermometer的數學!!!!!!

2012-02-13 3:29 am

There are some informations about the mercury column of a thermometer.

length temperature
3cm 20C
12cm 100C

(a)If the the mercury column is 5cm ,what is the correspnding temperature?
(b)When the temperature of the thermometer is 60C,how long is the mercury colimn?

Ans:
(a)Δθ / Δl
=100-20 / 12-3
=80/9
=8.89C/cm (1cm等於幾多度)

Δθ /Δl = 8.89
Δθ / 5-3 = 8.89
Δθ = 17.8C
therefore θ =20+17.8=37.8C

(b)Δθ / Δl = 8.89
60-20 / Δl = 8.89
Δl = 4.50cm
therefore l= 3+4.5 =7.5cm

(1)有顏色果d我5係好明點解係咁計,另外點解(a) length 要減但 (b) 就係temp.要減 ? 點解5係兩題都係剩減length or temp?

(2)仲有冇其他方法可以計?------->(可以5使答)

p.s.最好就答哂,如果真係5得ge 話就答得幾多得幾多la!!!!!^^
thx

更新1:

仲有冇其他ratio or other (no graph) ge 方法可以計?--------可以5使答

回答 (1)

天同

2012-02-13 8:24 am

✔ 最佳答案

1. Δθ and Δl are the change in temperature and length respectively. Because the reference temperature and reference length are 20'C and 3 cm respectively, hence, you have you substract the reference values (temperature or length) in order to get the change in temperature or length.

In (b), Δl is the change in length, which is found to be 4.5 cm
Because Δl = [length at 60'C - length at 20'C]
hence, length at 60'C = length at 20'C + Δl = (3 + 4.5) cm

2. You could use graphical method.
Suppose the two given points are plotted on a graph (temperature against length)to obtain a straight line, the equation for such straight line is given by (using "two-point form"),

T - 20/(100 - 20) = L - 3/(12 - 3)
where T is the temperature and L is the length of mercury column
hence, the line is represented by the equation:
T = 8.89L - 6.67

Having found the equation (which is called the "calibration curve"), the values of T or L can be calculated with given values of L or T respectively.

e.g. when the mercury column L = 5 cm
T = (8.89 x 5 - 6.67)'C = 37.8'C

when T = 60'C
60 = 8.89L - 6.67
L = (60+6.67)/8.89 cm = 7.5 cm

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