At 0^ C , the densities of wood and benzene are 880 kg m ⁻³ and 900 kg m ⁻³ , respectively. The coefficients of volume expansion for wood and benzene are 1.2 10⁻³ ^ C ⁻¹ and 1.5 10⁻³ ^ C ⁻¹ , respectively. Determine the temperature at which a piece of wood will just sink in benzene.

Step-by-step solution

For the piece of wood to just sink in benzene, the density of the wood must become equal to the density of benzene at that temperature T . The density of a substance at temperature T is given by: _T = ₀ 1 + T Equating the densities of wood and benzene at temperature T : _ wT = _ bT _ w0 1 + _w T = _ b0 1 + _b T Cross-multiplying, we get: _ w0 (1 + _b T) = _ b0 (1 + _w T) Substituting the given values: 880 (1 + 1.5 10⁻³ T) = 900 (1 + 1.2 10⁻³ T) 880 + 880 1.5 10⁻³ T = 900 + 900 1.2 10⁻³ T 880 + 1.32 T = 900 + 1.08 T