The coefficient of volume expansion of glycerin is 49 × 10−5 K−1 . The fractional decrease in its density for a 30o C rise in temperature will be

vtv0=1+ρΔt=1+49×10−5×30=1.0147070v0vt=11.01470Δρρ0=ρf−fρ0ρ0=m1vt−1v0mv0=v0vt−1Δρρ0=−0.0145=−1.45×10−2

The coefficient of volume expansion of glycerin is 49 × 10−5 K−1 . The fractional decrease in its density for a 30o C rise in temperature will be

vtv0=1+ρΔt=1+49×10−5×30=1.0147070v0vt=11.01470Δρρ0=ρf−fρ0ρ0=m1vt−1v0mv0=v0vt−1Δρρ0=−0.0145=−1.45×10−2

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The coefficient of volume expansion of glycerin is $49 \times 10^{- 5} K^{- 1}$ . The fractional decrease in its density for a $30^{o} C$ rise in temperature will be

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$1.45 \times 10^{- 2}$

$2 \times 10^{- 4}$

$3.5 \times 10^{- 3}$

$2.5 \times 10^{- 2}$

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$\frac{v_{t}}{v_{0}} = 1 + ρ Δ t = (1 + 49 \times 10^{- 5} \times 30) = 1.0147070$

$\frac{v_{0}}{v_{t}} = \frac{1}{1.01470}$

$\frac{Δ ρ}{ρ_{0}} = \frac{ρ_{f} - f ρ_{0}}{ρ_{0}} = \frac{m (\frac{1}{v_{t}} - \frac{1}{v_{0}})}{\frac{m}{v_{0}}} = \frac{v_{0}}{v_{t}} - 1$

$\frac{Δ ρ}{ρ_{0}} = - 0.0145 = - 1.45 \times 10^{- 2}$

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The coefficient of volume expansion of glycerin is 49 × 10−5 K−1 . The fractional decrease in its density for a 30o C rise in temperature will be

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The coefficient of volume expansion of glycerin is $49 \times 10^{- 5} K^{- 1}$ . The fractional decrease in its density for a $30^{o} C$ rise in temperature will be