Question

A U-tube filled with a liquid of volumetric coefficient of 10^-5/°C lies in a vertical plane. The height of liquid column in the left vertical limb is 100 cm. The liquid in the left vertical limb is maintained at a temperature = 0°C while the liquid in the right limb is maintained at a temperature = 100°C. Find the difference in levels in the two limbs.Pls help

Answer 1

use volume expansion concept ,
V=Vo (1+¥ dT)
we know volume directly proportional to length^3
so,
we can say that ,
V=kL^3
where k is proportionality constant .
now ,
kL^3=kLo^3 (1+¥ dT)
L^3=Lo^3 (1+¥ dT)
take cube root both side
L=Lo (1+¥ dT)^1/3
now use binomial expansion ,
L=Lo (1+¥/3.dT)
L=Lo +Lo ¥ dT/3

(L-Lo)=Lo ¥ dT/3
|----difference in level of limbs

now put
Lo=100cm
¥=10^-5 /·C
dT=(100-0)=100 C

hence difference in level of limbs =
100 x 10^-5 x 100/3=1/30 cm
= 3.33 x10^-2 cm

Answer 2

Let height difference be l

We know that T=100°C

l=L(alpha) T

l=100*10^-5×(100-0)

l=0.1cm