(Solved): Question 2. ( 4+3=7 marks): The diagram shows a schematic for a thermometer based on the expansion ...

Question 2. ( $4+3=7$ marks): The diagram shows a schematic for a thermometer based on the expansion of some fluid. There is a spherical reservoir of the fluid, with radius $R$, which is connected via a tube to a vertical section, with a circular cross section, radius $r$. (a) Assuming $r?R$, show that the change in fluid level in the tube is given by $?L=\frac{4}{3}\frac{?R^3?T}{r^2},$ where $?T$ is the change in temperature and $?$ is the volumetric expansion coefficient of the fluid. (b) What properties should the system (ie apparatus and fluid) have to be most sensitive?