Concept explainers
An ordinary glass is filled to the brim with 450.0 mL of water at 100.0°C. If the temperature of glass and water is decreased to 20.0°C, how much water could be added to the glass?
The additional volume of water that can be added to the glass after the decrease in temperature
Answer to Problem 13P
Solution:
The additional volume of water that can be added to the glass is 6.588 ml
Explanation of Solution
Given:
Initial volume of glass,
Initial volume of water,
Initial temperature,
Final temperature,
Formula used:
, where Vi is the initial volume and β is the coefficient of volume expansion
Calculation:
The relation between change in volume of a substance (ΔV)and change in temperature (ΔT)is given by,
, where Vi is the initial volume and β is the coefficient of volume expansion
Here, , where Vf is final volume
where Tf is final temperature and Ti is initial temperature
For glass,
Therefore,
For water,
Therefore,
This shows that while the volume of water has come down to 442.44 ml, the volume of glass is 449.028 ml
Therefore, additional water that can be added to the glass is,
(Note that while the above steps are for a clearer illustration of the problem, we can obtain this result by just subtracting ΔVg from ΔVw also)
Chapter 13 Solutions
Physics: Principles with Applications
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