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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?
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Solution
Given:
Density of wood at 0 °C, fw = 880 kgm-3
Density of benzene at 0 °C, fb = 900 kgm-3
Coefficient of volume expansion for wood, γw = Coefficient of volume expansion for benzene, γb = 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 = T2-T1.
The piece of wood begins to sink when its weight is equal to the weight of the benzene displaced.
Mass = volume × density
Therefore, Vfwg = Vfbg
`=> 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.
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