Question: The coefficient, β, of thermal expansion of a liquid relates the change in the volume V (in m3) of a fixed quantity of a liquid to an increase in its temperature T (in °C):
dV = βV dT
(a) Let ρ be the density (in kg/m3) of water as a function of temperature. (For a mass m of liquid, we have ρ = m/V.) Write an expression for dρ in terms of ρ and dT.
(b) The graph in Figure shows density of water as a function of temperature. Use it to estimate β when T = 20°C and when T = 80°C.
