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At 0 deg C the densities of wood and benzene are 880 kg/m³ and 900 kg/m³ respectively. Their coefficients of volume (cubical) expansion are 1.2*10⁻³ per deg C for wood and 1.5*10⁻³ per deg C for benzene. At what temperature will a block of wood just begin to sink in benzene?

1. 83 deg C
2. 47 deg C
3. -47 deg C
4. -83 deg C

Correct answer: 83 deg C

Solution

Benzene expands faster than wood (larger gamma), so as temperature rises benzene's density falls faster. At a certain temperature the benzene becomes less dense than the wood, and the wood just sinks. Setting the two temperature-dependent densities equal gives that temperature.

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