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Properties of Matter question

2013 · Q157
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Properties of Matter question

2013 · Q157

NEETPhysicsProperties of MatterMCQ+4 / −1
The density of water at 20oC is 998 kg/m3 and at 40oC is 992 kg/m3. The coefficient of volume expansion of water is
  1. A
    3 ×\times× 10−-−4/oC
  2. B
    2 ×\times× 10−-−4/oC
  3. C
    6 ×\times× 10−-−4/oC
  4. D
    10 ×\times× 10−-−4/oC
View written solutionFree

Correct answer: A

From question,

Δρ\Delta \rho Δρ = (998 – 992) kg/m3 = 6 kg/m3

ρ=998+9922kg/m3=995 kg/m3\rho = {{998 + 992} \over 2}kg/{m^3} = 995\,kg/{m^3}ρ=2998+992​kg/m3=995kg/m3

ρ=mv\rho = {m \over v}ρ=vm​

⇒Δρρ=−ΔVV⇒∣Δρρ∣=∣ΔVV∣ \Rightarrow {{\Delta \rho } \over \rho } = - {{\Delta V} \over V} \Rightarrow \left| {{{\Delta \rho } \over \rho }} \right| = \left| {{{\Delta V} \over V}} \right|⇒ρΔρ​=−VΔV​⇒​ρΔρ​​=​VΔV​​

∴\therefore∴ Coefficient of volume expansion of water,

1VΔVΔt=1ρΔρΔt=6995×20≈3×10−4/oC{1 \over V}{{\Delta V} \over {\Delta t}} = {1 \over \rho }{{\Delta \rho } \over {\Delta t}} = {6 \over {995 \times 20}} \approx 3 \times {10^{ - 4}}{/^o}CV1​ΔtΔV​=ρ1​ΔtΔρ​=995×206​≈3×10−4/oC

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