The coefficient of volume expansion of glycerin is 49xx10^(-5)K^(-1). What is the fractional change in its density for a 30^(@)C rise in temperature ?

The coefficient of volume expansion of glycerin is 49xx10^(-5)K^(-1).

1.	The coefficient of volume expansion of glycerin is 49xx10^(-5)K^(-1). What is the fractional change in its density for a 30^(@)C rise in temperature ?
Answer» Solution :IF volume glycerine becomes V with increase in TEMPERATURE by `30^(@)C`, then `V=V_(0)(1+gammaDeltaT)` But `V=(M)/(rho)` and `V_(0)=(M)/(rho_(0))`, `:.(M)/(rho)=(M)/(rho_(0))(1+gammaDeltaT)` `:.(rho)/(rho_(0))=1/((1+gammaDeltaT))` `:.(rho-rho_(0))/(rho_(0))=(1-1-gammaDeltaT)/(1+gammaDeltaT)` `:.(rho-rho_(0))/(rho_(0))=(-gammaDeltaT)/(1+gammaDeltaT)` `=(-49xx10^(-5)xx30)/(1+49xx10^(-5)xx30)` `(Delta rho)/(rho_(0))=-0.0145` Negative SIGN REPRESENTS the decrease in density `=0.0145~~1.5xx10^(-2)`