The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is . What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures?
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When there is no change in liquid level in vessel then eal . vesse
Change in volume in liquid relative to vessel
Suppose, height of liquid in each arm before rising the temperature is .
With temperature rise height of liquid in each arm increases i.e. and
Also
.
A pendulum clock loses a day if the temperature is and gains a day if the temperature is . The temperature at which the clock will show correct time, and the co-efficient of linear expansion of the metal of the pendulum shaft are respectively:
Time lost/gained per day second
On dividing we get,
The apparent coefficient of expansion of a liquid when heated in a copper vessel is and that when heated in a silver vessel is . If is the linear coefficient of expansion of copper, then the linear coefficient of expansion of silver is
where coefficient of real expansion, coefficient of apparent expansion and coefficient of expansion of vessel.
For copper:
For silver,
The coefficient of linear expansion for a certain metal varies with temperature as . If is the initial length of the metal and the temperature of metal is changed from to , then
As, .
The length of a metallic rod is at and becomes , on heating upto . The linear expansion of the metal will be
A solid metallic cube having total surface area is uniformly heated. If its temperature is increased by , calculate the increase in volume of the cube.
(Given : )
We have
Now, Total surface area of cube
So,
The coefficient of apparent expansion of mercury in a glass vessel is and in a steel vessel is . If for steel is , then that of glass is
So
Further,
The value of coefficient of volume expansion of glycerine is . The fractional change in the density of glycerine for a rise of in its temperature, is:
0.020
0.025
0.010
0.015
From question,
Rise in temperature
Fractional change in the density ?
A rod of length is pivoted at an end and freely rotated in a horizontal plane at an angular speed about a vertical axis passing through . Coefficient of linear expansion of material of rod is . Find the percentage change in its angular velocity if temperature of system is increased by is
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