The densities of wood and benzene at 0^ C are 880 ~kg ~m ⁻³ and 900 ~kg ~m ⁻³ , respectively. The coefficient of volume expansion is 1.2 10⁻³ C ⁻¹⁰ for wood and 1.5 10⁻³⁰ C ⁻¹ for benzene. Then the temperature at which a piece of wood just

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The densities of wood and benzene at 0^ C are 880 ~kg ~m ⁻³ and 900 ~kg ~m ⁻³ , respectively. The coefficient of volume expansion is 1.2 10⁻³ C ⁻¹⁰ for wood and 1.5 10⁻³⁰ C ⁻¹ for benzene. Then the temperature at which a piece of wood just sinks in benzene is

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Correct answer: C. 83.3^ C

Given, density of wood at 0^ C , _w=880 Kg m ⁻³ density of benzene at 0^ C , _b=900 ~kg ~m ⁻³ coefficient of volume expansion of wood, _w=1.2 10^ -3 C ⁻¹ coefficient of volume expansion of benzene, _b=1.5 10⁻³ ^ C ⁻¹ and initial temperature, T₁=0^ C Let T₂ be the temperature at which pieces of wood will just sink in benzene and T=T₂-T₁ The piece of wood begins to sink when it weight is equal to the weight of benzene displaced. Mass = Volume Density Therefore, V _w g=V _b g aligned & _w 1+ _w T = _b 1+ _b T & 880 1+

The densities of wood and benzene at 0^ C are 880 ~kg ~m ⁻³ and 900 ~kg ~m ⁻³ , respectively. The coefficient of volume expansion is 1.2 10⁻³ C ⁻¹⁰ for wood and 1.5 10⁻³⁰ C ⁻¹ for benzene. Then the temperature at which a piece of wood just sinks in benzene is

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