At a temperature 20°C the volume of a certain glass flask up to a certain mark on the stem of the flask,
is exactly 100 cm. The flask is filled up to this mark with a liquid at 20°C. The cross section of the stem
is 1 mm- and can be considered constant. How far will the liquid rise or fall in the stem when the
temperature is raised to 40°C? Given, volume expansion coefficient of the liquid is 120 x 10 per 'c,
and linear expansion coefficient of glass is 8 * 10 per degree c.
Answers
Explanation:
Volume expansion coefficient of glass=3×linear=3α
Change in temperature is 38−18=200C
Increment of volume of flask is ΔV=50cc×3α×200C=0.027cc
Expansion in mercury 50cc×γΔt=50×180×10−6×20=0.180cc
Apparent increment=0.180−0.027=0.153cc
Option C is correct.
Given:
Initial temperature = 20°C
Final temperature = 40°C
Initial height of liquid = 100 cm
Cross section of the stem = 1mm
Coefficient of volume expansion = 120 * 10^-3/°C
Coefficient of linear expansion = 8* 10^-3/°C
To find:
How far will the liquid rise or fall.
Solution:
The formula for linear expansion is:
ΔL = α L ΔT
Where ΔL = change in length
α = linear expansion of coefficient
L = initial length
ΔT = change in temperature
L- 100 = 8*10 * 100 (40 - 20)
L - 100 = 8 * 10^-3 * 100 * (20)
L - 100 = 16
L = 116 cm
Therefore, the liquid will rise up to 116 cm.