The coefficient of volume expansion of benzene and wood are 1.2 x 10^-3/ °C and 1.5 x 10^-4/°C. At 0°C their densities are 9 x 10^2 kg/ m^3 and 8.8 x 10^2 kg/m^3. At what temperature wood will sink in benzene ?
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Answer:
Let the volume of wood be V
W
and mass be m
W
.
So ρ
w
=
V
W
m
W
=8.8×10
2
....(1)
Let the volume of benzene be V
b
and mass be m
b
.
So ρ
b
=
V
b
m
b
=9×10
2
....(1)
When the Temperature is increased by ΔT,
Volume of wood be V
W1
=V
W
(1+γ
wood
ΔT)
and mass be m
W
So ρ
w1
=
V
W
(1+γ
wood
ΔT)
m
W
=
(1+γ
wood
ΔT)
8.8×10
2
....(3)
Volume of benzene be V
b1
=V
b
(1+γ
benzene
ΔT)
and mass be m
b
.
So ρ
b1
=
V
b
(1+γ
benzene
ΔT)
m
b
=
(1+γ
benzene
ΔT)
9×10
2
..(4)
So if both densities become same, wood will start sinking i.e. ρ
w1
=ρ
b1
(1+1.5×10
−4
ΔT)
8.8×10
2
=
(1+1.2×10
−3
ΔT)
9×10
2
ΔT=21.70
0
C
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