Question

Miss Takken heats a 300 g piece of iron to a temperature of 500 degrees Celsius and then plunges it into a vat of 30 L of water at 5 degrees Celsius. What is the final temperature of the system?

Answer 1

The final temperature for water and iron will be the same, $t_i$.

Heat given by iron to water:

$$Q_1=c_im_i(t_{f}-t_{ii}),$$

heat received by water:

$$Q_2=c_wm_w(t_{f}-t_{iw}),$$

and, as we know, thermal equilibrium is

$$Q_1+Q_2=0,\\ c_im_i(t_{f}-t_{ii})+c_im_i(t_{f}-t_{iw})=0,\\\space\\ t_f=\frac{c_im_it_{ii}+c_wm_wt_{iw}}{c_im_i+c_wm_w}=5.5°\text C.$$