Answer to Question #157458 in Physics for Hidayu

Question

Mr Warner is hiding a 1500 g of gold bar with a temperature of 30 °C inside a tank full of water with a temperature of 97 °. If the mass of water is 30 kg, calculate the final temperature of the gold bar. Given specific heat capacity of gold is 129 J/kg °C and water is 4200 J/kg °C

Answer 1

While water heats up the gold bar (temperature of water decreases), the gold bar heats up (temperature of gold increases). The final temperature of water and gold will be the same in thermal equilibrium:

$$Q_g=c_gm_g(t_f-t_g),\\ Q_w=c_wm_w(t_f-t_w),\\ Q_g+Q_w=0,\\ c_gm_g(t_f-t_g)+c_wm_w(t_f-t_w)=0,\\\space\\ t_f=\frac{c_gm_gt_g+c_wm_wt_w}{c_gm_g+c_wm_w}=96.9°\text{C}.$$