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–1 for benzene. At what temperature will a piece of wood just sink in benzene?

Answer 1

At 83.2 °C temperature a piece of wood just sink in benzene.

Given-

• Density of wood at 0 °C = 880 kg /m³
• Density of benzene at 0 °C = 900 kg /m³
• Coefficient of volume expansion for wood = 1.2 × 10⁻³/ °C

• Coefficient of volume expansion for benzene = 1.5 × 10⁻³/ °C

When densities of both the substance will be same in that case a piece of wood will just sink.

So V will become (1 + γΔT) and

Density (ρ) will become 1 / (1 + γΔT)

Let the temperature be T °C

So, By substituting the value we get

880 / 1 + 1.2 × 10⁻³ T = 900 /  1 + 1.5 × 10⁻³ T

By solving the above equation we get

T = 83.2 °C