The densities of wood and benzene at `0^(@)C` are `880 kg//m^(3)` and `900 kg//m^(3)` respectively. The coefficients of volume expansion are `1.2 xx 10^(-3)//'^(@)C` for wood and `1.5 xx 10^(-3)//'^(@)C` for benzene. At what temperature will a piece of wood just sink in benzene?

Explanation

To find the temperature at which a piece of wood just sinks in benzene, we need to equate the densities of wood and benzene as they expand with temperature. Here’s a step-by-step solution:

### Step 1: Write down the given data
- Density of wood, \( \rho_w = 880 \, \text{kg/m}^3 \)
- Density of benzene, \( \rho_b = 900 \, \text{kg/m}^3 \)
- Coefficient of volume expansion for wood, \( \gamma_w = 1.2 \times 10^{-3} \, \text{°C}^{-1} \)
- Coefficient of volume expansion for benzene, \( \gamma_b = 1.5 \times 10^{-3} \, \text{°C}^{-1} \)

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