Problem $1$: Assume that a thermometer with a spherical test section of radius $r=0\mathrm{.}3cm$ is initially at a temperature

$T_i=50C,$ the density of the thermometer medium is $=1000k\frac{g}{m^3},$ its specific heat is $c=3000\frac{J}{k}gC,$ the heat transfer

coefficient $h=1500\frac{W}{m^{2o}}C,$ the initial temperature of the surroundings $T_0=100C,$ and the rate of change of the sur$-$

roundings temperature $=5\frac{C}{s}.$ 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.