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Question

In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures t subscript 1 end subscript and t subscript 2 end subscript. The liquid columns in the two arms have heights l subscript 1 end subscript and l subscript 2 end subscript respectively. The coefficient of volume expansion of the liquid is equal to

  1. fraction numerator l subscript 1 end subscript minus l subscript 2 end subscript over denominator l subscript 2 end subscript t subscript 1 end subscript minus l subscript 1 end subscript t subscript 2 end subscript end fraction    
  2. fraction numerator l subscript 1 end subscript minus l subscript 2 end subscript over denominator l subscript 1 end subscript t subscript 1 end subscript minus l subscript 2 end subscript t subscript 2 end subscript end fraction    
  3. fraction numerator l subscript 1 end subscript plus l subscript 2 end subscript over denominator l subscript 2 end subscript t subscript 1 end subscript plus l subscript 1 end subscript t subscript 2 end subscript end fraction    
  4. fraction numerator l subscript 1 end subscript plus l subscript 2 end subscript over denominator l subscript 1 end subscript t subscript 1 end subscript plus l subscript 2 end subscript t subscript 2 end subscript end fraction    

The correct answer is: fraction numerator l subscript 1 end subscript minus l subscript 2 end subscript over denominator l subscript 2 end subscript t subscript 1 end subscript minus l subscript 1 end subscript t subscript 2 end subscript end fraction


    Suppose, height of liquid in each arm before rising the temperature is l.

    With temperature rise height of liquid in each arm increases i.e. l1 > l and l2 > l
    Also l equals fraction numerator l subscript 1 end subscript over denominator 1 plus gamma t subscript 1 end subscript end fraction equals fraction numerator l subscript 2 end subscript over denominator 1 plus gamma t subscript 2 end subscript end fraction
    Þ l subscript 1 end subscript plus gamma l subscript 1 end subscript t subscript 2 end subscript equals l subscript 2 end subscript plus gamma l subscript 2 end subscript t subscript 1 end subscript Þ gamma equals fraction numerator l subscript 1 end subscript minus l subscript 2 end subscript over denominator l subscript 2 end subscript t subscript 1 end subscript minus l subscript 1 end subscript t subscript 2 end subscript end fraction

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