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Grade 12th passMechanics

A glass flask of volume 200 cm^3 is just filled with mercury at 20°C . The amount of mercury that will overflow when the temperature of the system raised at 100°C is

Pooja kandpal

8 Years agoGrade 12th pass

1 Answer

Arun

Approved Tutor Answer8 Years ago

Dear Pooja

If depends on:

a) if you are allowed to ignore the expansion of the glass, and if not, what type type of glass is used (note ignoring the expansion of the glass introduces a 10% error approx.)

b) what value(s) are used for the volume expansion coefficients.

Note that the volume expansion coefficient (β) of a material is 3 times its linear expansion coefficient (α). β = 3α.
________________________

Using values from the link:
volume expansion coefficient of glass = 3 x 5.9x10⁻⁶ K⁻¹
volume expansion coefficient of mercury = 3 x 61x10⁻⁶ K⁻¹

The amount of overflow depends on the difference between these, which is
3x10⁻⁶ x (61-5.9) = 1.653x10⁻⁴ K⁻¹

So the mercury expands more than the glass by an amount:
200 x 1.653x10⁻⁴ x (100 – 20) = 2.6cm³
This is the amount that overflows.

Regards

Arun (askIITians forum expert)

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