The co-efficient of apparent expansion of a liquid in a vessel A is 18- 10-4-oC and in vessel B is 21- 10-4-oC- The difference in the coefficients of linear expansions of A and B is -

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Standard X

Physics

Expansion In Liquids and Gases

The co-effici...

Question

The co-efficient of apparent expansion of a liquid in a vessel A is $18 \times 10^{- 4} /^{o} C$ and in vessel B is $21 \times 10^{- 4} /^{o} C$ . The difference in the coefficients of linear expansions of A and B is :

1 \times 10^{- 3} /^{o} C

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1 \times 10^{- 6} /^{o} C

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1 \times 10^{- 5} /^{o} C

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1 \times 10^{- 4} /^{o} C

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Solution

The correct option is B $1 \times 10^{- 4} /^{o} C$
$γ_{r} = γ_{a} + γ_{g} = γ_{a} + 3 α_{g}$
$γ_{r} = γ_{a 1} + 3 α_{1} = γ_{a 2} + 3 α_{2}$ for both vessels A and B
$∴ 18 \times 10^{- 4} + 3 α_{1} = 21 \times 10^{- 4} + 3 α_{2}$
$∴ 3 (α_{1} - α_{2}) = 3 \times 10^{- 4}$
$∴ α_{1} - α_{2} = 1 \times 10^{- 4}$ / $^{0}$ C

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The co-efficient of apparent expansion of a liquid in a vessel A is 18×10−4/oC and in vessel B is 21×10−4/oC. The difference in the coefficients of linear expansions of A and B is :

The correct option is B 1×10−4/oCγr=γa+γg=γa+3αgγr=γa1+3α1=γa2+3α2 for both vessels A and B∴18×10−4+3α1=21×10−4+3α2∴3(α1−α2)=3×10−4∴α1−α2=1×10−4/ 0C

The co-efficient of apparent expansion of a liquid in a vessel A is $18 \times 10^{- 4} /^{o} C$ and in vessel B is $21 \times 10^{- 4} /^{o} C$ . The difference in the coefficients of linear expansions of A and B is :