Heat and Thermodynamics 2 Question 7

10. A cube of coefficient of linear expansion αs is floating in a bath containing a liquid of coefficient of volume expansion γl. When the temperature is raised by ΔT, the depth upto which the cube is submerged in the liquid remains the same. Find the relation between αs and γl showing all the steps.

(2004, 2M)

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Answer:

Correct Answer: 10. βl=β(w0w1w0w2)+(w2w1)(w0w2)(T2T1)

Solution:

  1. When the temperature is increased, volume of the cube will increase while density of liquid will decrease. The depth upto which the cube is submerged in the liquid remains the same.

Upthrust = Weight. Therefore, upthrust should not change

F=FViρLg=ViρLg(Vi= volume immersed )(Ahi)(ρL)(g)=A(1+2αsΔT)(hi)(ρL1+γlΔT)g

Solving this equation, we get γl=2αs



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