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Question

A non-conducting body floats in a liquid at 20C with 23 of its volume immersed in the liquid. When liquid temperature is increased to 100C, 34 of body's volume is immersed in the liquid. Then the coefficient of real expansion of the liquid is (neglecting the expansion of the container):

A
15.6×104 C1
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B
156×104 C1
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C
1.56×104 C1
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D
0.156×104 C1
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Solution

The correct option is D 15.6×104 C1
From Archimedes' principle, weight of the body is balanced by the weight of the liquid displaced.
At 20oC, ρbVbg=ρl1×23Vbg.........(i)
At 100oC, ρbVbg=ρl2×34Vbg........(ii)
From (i) and (ii),
ρl1ρl2=98.........(iii)

From Law of conservation of mass, total mass of liquid is constant.
Ml1=Ml2
ρl1Vl1=ρl2Vl2..........(iv)

Volume expansion of liquid is governed by,
Vl2=Vl1(1+γΔT)...........(v)

From (iv) and (v),
ρl1ρl2=1+γΔT...........(vi)

Solving, (iii) and (vi),
γ=15.6×104 oC1

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