   Chapter 10, Problem 61AP

Chapter
Section
Textbook Problem

A liquid with a coefficient of volume expansion of β just fills a spherical flask of volume V0 at temperature Ti (Fig. P10.61). The flask is made of a material that has a coefficient of linear expansion of α. The liquid is free to expand into a capillary of cross-sectional area A at the top. (a) Show that if the temperature increases by ΔT, the liquid rises in the capillary by the amount Δh = (V0/A)(β − 3α)ΔT. (b) For a typical system, such as a mercury thermometer, why is it a approximation to neglect the expansion of the flask? Figure P10.61

(a)

To determine
The rise in the liquid ( Δh ).

Explanation

Given info: The co-efficient of volume expansion of the liquid is β . The volume of the spherical flask is V0 . The temperature of the flask is Ti . The co-efficient of linear expansion of the flask is α . The cross sectional area of the capillary is A. The temperature increases by ΔT .

Formula for the overflow volume is,

Vof=AΔh (I)

Overflow volume is also given by,

Vof=ΔVlΔVf (II)

• ΔVl is the change in volume of the liquid.
• ΔVf is the change in volume of the flask.

Formula to calculate ΔVl is,

ΔVl=βVoΔT (III)

Formula to calculate ΔVf is,

ΔVf=3αVoΔT (IV)

Substitute Equations (III) and (IV) in (II)

(b)

To determine
Why the expansion of the flask is neglected for mercury.

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