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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Thermal Properties of Matter

NTA Abhyas 2020 · Physics · Thermal Properties of Matter

When a liquid in a glass vessel is heated, its apparent expansion...

When a liquid in a glass vessel is heated, its apparent expansion coefficient is 10.30×10−4℃−110.30 \times {10}^{- 4}{℃}^{- 1}. When the same liquid is heated in a metal vessel, its apparent expansion coefficient is 10.06×10−4℃−1.10.06 \times {10}^{- 4}{℃}^{- 1}. If the coefficient of linear expansion of glass = 9×10−6℃−1,9 \times {10}^{- 6}{℃}^{- 1}, what is the coefficient of linear expansion of metal?

Options

  1. A51×10−6℃−151 \times {10}^{- 6}{℃}^{- 1}
  2. B17×10−6℃−117 \times {10}^{- 6}{℃}^{- 1}
  3. C25×10−6℃−125 \times {10}^{- 6}{℃}^{- 1}
  4. D43×10−6℃−143 \times {10}^{- 6}{℃}^{- 1}

Correct answer

B. 17×10−6℃−117 \times {10}^{- 6}{℃}^{- 1}

Step-by-step solution

Here, γag=10.30×10−4℃−1{γ}_{ag} = 10.30 \times {10}^{- 4}{℃}^{- 1}

γam=10.06×10−4℃−1{γ}_{am} = 10.06 \times {10}^{- 4}{℃}^{- 1}

αg=9×10−6℃−1,αm=?{α}_{g} = 9 \times {10}^{- 6}{℃}^{- 1}, {α}_{m} = ?

Now, γr=γag+γg=γam+γm{γ}_{r} = {γ}_{ag} + {γ}_{g} = {γ}_{am} + {γ}_{m}

∴10.30×10−4+3×9×10−6=10.06×10−4+γm[∵γg=3×αa]∴ 10.30 \times {10}^{- 4} + 3 \times 9 \times {10}^{- 6} = 10.06 \times {10}^{- 4} + {γ}_{m} [ ∵ {γ}_{g} = 3 \times {α}_{a} ]

∴γm=(10.30+0.27−10.06)10−4=0.51×10−4∴ {γ}_{m} = \left(10.30 + 0.27 - 10.06\right){10}^{- 4} = 0.51 \times {10}^{- 4}

αm=13γm=0.51×10−43{α}_{m} = \dfrac{1}{3}{γ}_{m} = \dfrac{0.51 \times {10}^{- 4}}{3}

= 0.17×10−4=17×10−6℃−10. 17 \times {10}^{- 4} = 17 \times {10}^{- 6}{℃}^{- 1}
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