Using the following data- at what temperature will the wood just sink in benzene-Density of wood at 0- C - 8-8 - 10 2 k g - m 3Density of benzene at 0- C - 9 - 10 2 k g - m 3 cubical expansivity of wood 1-5 - 10 - 4 K - 1 cubical expansivity of benzene 1-2 - 10 - 3 K - 1

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Byju's Answer

Standard XII

Physics

Area and Volume Expansion

Using the fol...

Question

Using the following data, at what temperature will the wood just sink in benzene?
Density of wood at $0^{\circ} C = 8.8 \times 10^{2} k g / m^{3}$
Density of benzene at $0^{\circ} C = 9 \times 10^{2} k g / m^{3}$
cubical expansivity of wood $1.5 \times 10^{- 4} K^{- 1}$
cubical expansivity of benzene $1.2 \times 10^{- 3} K^{- 1}$

27^{\circ} C

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{21.7}^{\circ} C

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31^{\circ} C

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{31.7}^{\circ} C

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Solution

The correct option is A $27^{\circ} C$

Wood will start to sink in benzene when its density is just greater than benzene
so Temperature at which this will happen can be found out by equating their density at temperature $T$

$D = \frac{m a s s}{v o l u m e}$

$D = D_{O} (1 - γ Δ T)$

Equating densities at Temprature $T$
$8.8 \times 10^{2} (1 - 1.5 \times 10^{- 4} (T - 0)) = 9 \times 10^{2} \times (1 - 1.2 \times 10^{- 3} (T - 0))$

solving the above equation.
$T = {21.7}^{o} C$

Option $(B)$ is correct

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Similar questions

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Using the following data, at what temperature will the wood just sink in benzene?Density of wood at 0∘C=8.8×102kg/m3Density of benzene at 0∘C=9×102kg/m3 cubical expansivity of wood 1.5×10−4K−1 cubical expansivity of benzene 1.2×10−3K−1