The value of coefficient of volume expansion of glycerin is 5 ×10-4 K-1 . The fractional change in the density of glycerin for a rise of 40°C in its temperature, is
Question
The value of coefficient of volume expansion of glycerin is 5 ×10-4 K-1 . The fractional change in the density of glycerin for a rise of 40°C in its temperature, is
Solution
The coefficient of volume expansion (β) is given as 5 × 10^-4 K^-1. This means that for every degree rise in temperature, the volume of glycerin increases by this fraction.
The fractional change in volume ΔV/V is given by βΔT, where ΔT is the change in temperature.
So, ΔV/V = βΔT = 5 × 10^-4 K^-1 × 40 K = 0.02.
The density of a substance is inversely proportional to its volume. So, if the volume increases by a certain fraction, the density decreases by the same fraction.
Therefore, the fractional change in density Δρ/ρ is equal to -ΔV/V.
So, Δρ/ρ = -0.02.
Therefore, the fractional change in the density of glycerin for a rise of 40°C in its temperature is -0.02 or -2%.
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