Question

The densities of wood  and benzene at 0°C are 880 kg m³ and 900 kg m^–3 , respectively. The coefficients of volume expansion are 1.2 × 10^–3 °C^–1 for wood and 1.5 × 10^–3 °C^–1for benzene. At what temperature will a piece of wood just sink in benzene?

Answer 1

Given:
Density of wood at 0 °C, f_w = 880 kgm^​-3
Density of benzene at 0 °C, f_b = 900 kgm^-​3
Coefficient of volume expansion for wood, γ_w = Coefficient of volume expansion for benzene, γ_b = 1.5 × 10^–3 °C^–1
So, initial temperature, T₁ = 0 °C
Let T₂ be the temperature at which the piece of wood will just sink in benzene and ΔT = T_2-T₁.
The piece of wood begins to sink when its weight is equal to the weight of the benzene displaced.
Mass = volume × density

Therefore, Vf_wg = Vf_bg

`=> f_w/(1+γ_w ΔT) = f_b/(1+γ_bΔT)`

`=> 880/(1+1.2×10^-3ΔT) = 900/(1+1.5×10^-3ΔT)`

⇒ 880+880 × 1.5 × 10^-3 ΔT =900+900 ×1.2×10^-3 ΔT

⇒ (1320 -1080)× 10^-3 ΔT =20

⇒ ΔT = 83.3°C

⇒ T₂ -T₁ ≅ 83°

⇒ T₂ -0° ≅ 83°

⇒ T₂ ≅ 83°C

Therefore, the piece of wood will just sink in benzene at 83 ^oC.