Problem 1: Assume that a thermometer with a spherical test section of radius $r = 0.3cm$ is initially at a temperature $T_i=50^\circ C$, the density of the thermometer medium is $\rho =1000kg/m^3$, its specific heat is $c=3000J/kg^\circ C$, the heat transfer coefficient $h=1500W/m^2^\circ C$, the initial temperature of the surroundings $T_0=100^\circ C$, and the rate of change of the surroundings temperature $\alpha = 5^\circ C/s$. How does the temperature of the thermometer compares to that of the surrounding medium at long times? Plot the ratio of the thermometer's temperature to the surrounding temperature as a function of time.
