The coefficient of volume expansion of glycerin is 49x10⁻⁵K⁻¹. What is the fractionalchange in its density for a 30°C rise in temperature?
Question
The coefficient of volume expansion of glycerin is 49x10⁻⁵K⁻¹. What is the fractionalchange in its density for a 30°C rise in temperature?
Solution
The coefficient of volume expansion (β) is given as 49x10⁻⁵K⁻¹ and the change in temperature (ΔT) is 30°C.
The fractional change in volume (ΔV/V) due to a change in temperature can be calculated using the formula:
ΔV/V = β * ΔT
Substituting the given values:
ΔV/V = 49x10⁻⁵K⁻¹ * 30K = 0.0147
Since density (ρ) is inversely proportional to volume (V), the fractional change in density (Δρ/ρ) is equal to the negative of the fractional change in volume:
Δρ/ρ = - ΔV/V = -0.0147
So, the fractional change in density for a 30°C rise in temperature is -0.0147 or -1.47%.
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