Answer to Question #290661 in Physics for JAY KIN

Question

A cup is made from 200 g of silver and contains 200 g of water. Both cup and water are at room temperature (24^oC). A 40-g piece of unknown material is heated to 85^oC and then added to the water. The heat released to the environment by the cup, water, and object system is negligible. After achieving thermal equilibrium, all three objects have a temperature of 25^oC. What is the specific heat of the unknown material?1.      For water, c = 4186 J/kg.C^o. For silver, c = 235 J/kg.C^o

Answer 1

$$c_sm_s(t_f-t_r)+c_wm_w(t_f-t_r)+cm(t_f-t)=0,\\\space\\ c=\dfrac{c_sm_s(t_f-t_r)+c_wm_w(t_f-t_r)}{m(t-t_f)},\\ c=368\text{ J}/\text{(kg}·\text K).$$