The value of coefficient of volume expansion of glycerin is 5 xx 10^(-4) K^(-1). The fractional change in the density of glycerin for a rise of 40^@ C in its temperature is _____

The value of coefficient of volume expansion of glycerin is 5 xx 10^(-

1.	The value of coefficient of volume expansion of glycerin is 5 xx 10^(-4) K^(-1). The fractional change in the density of glycerin for a rise of 40^@ C in its temperature is _____
Answer» `0.010` `0.015` `0.020` `0.025` Solution :SUPPOSE final DENSITY is `d_f` and initial density is `d_i`. `therefore d_f=(di)/(1+gammaDeltaT)rArr d_i/d_f =(1-gammaDeltaT)`…(1) Fractional change in density =`(d_i-d_f)/d_i` `=1-d_f/d_i` `=1-(1-gamma DeltaT)^(-1)` USING binomial theorem for EXPANSION from equation (1), `=1-(1-gammaDeltaT)` `=gamma DeltaT` `=5xx10^(-4)xx40` `=2XX10^(-2)` =0.020