Question

A one litre glass flask contains some mercury and it is found that at different temperatures the volume of air inside the flask remains the same. What is volume of mercury in this flask if coefficient of linear expansion of the glass is $ 9 \times {10^{ - 6}}{C^{{ \circ ^{ - 1}}}} $ while of volume expansion of mercury is $ 1.8 \times {10^{ - 4}}{C^{{ \circ ^{ - 1}}}} $ .

Answer 1

Hint: before solving the problem we should know about the following term.
Coefficient of linear expansion: The ratio of change in length for $ 1 $ degree rise in temperature is called the coefficient of linear expansion.
Coefficient of volume expansion: The ratio of change in volume for $ 1 $ degree rise in temperature is called the coefficient of volume expansion.
Coefficient of volume expansion $ = 3 \times $ Coefficient of linear expansion.

Complete step by step solution:
Here,
Coefficient of linear expansion of the glass $ = 9 \times {10^{ - 6}}{C^{{ \circ ^{ - 1}}}} $ .
So, Coefficient of volume expansion of the glass $ = 3 \times 9 \times {10^{ - 6}}{C^{{ \circ ^{ - 1}}}} $ .
Coefficient of volume expansion of the mercury $ = 1.8 \times {10^{ - 4}}{C^{{ \circ ^{ - 1}}}} $ .
Volume of flask $ = 1000ml $
As, volume in the air flask remains the same.
It means that the expansion of the flask is equal to the expansion of mercury.
So,
  $ {V_g}{\gamma _g}t = {V_m}{\gamma _m}t $
  $ \Rightarrow {V_m} = \dfrac{{{V_g}{\gamma _g}}}{{{\gamma _m}}} $
By keeping value in it. We get,
  $ \Rightarrow {V_m} = 1000\dfrac{{(3 \times 9 \times {{10}^{ - 6}})}}{{1.8 \times {{10}^{ - 4}}}} $
  $ \Rightarrow {V_m} = 150ml $
So, from the above calculation we had got, $ {V_m} = 150ml $ .

Note:
Lowering of temperature again bends the strip, but with the metal of smaller linear coefficient of expansion at the outer side. Such strips will be used in electric iron, electric ovens, and refrigerators to control the temperature. When the hot glass is touched with a cold knife. Some processes in nature are due to continued expansion and contraction of size like formation of soil from rock is called weathering.