Question

An aluminum cup with mass 0.59 kg holds 0.38 kg of water. Both the cup and the water have a temperature of 15.°C. If a 0.62-kg piece of copper at 61.°C is added to the cup, what is the final equilibrium temperature in °C? You may assume that the cup, water, and copper are well insulated from anything else.

Answer 1

To find the final equilibrium temperature, use the principle of conservation of energy and the specific heat capacities of the substances. Set up an equation and solve for the final temperature, which after calculation is found to be 21.4°C.

Step-by-step explanation:

To find the final equilibrium temperature, we can use the principle of conservation of energy and the specific heat capacities of the substances involved. The total heat gained by the water and copper must equal the heat lost by the aluminum cup. Assuming no heat is lost to the surroundings, we can set up the equation:

Heat gained by water + Heat gained by copper = Heat lost by aluminum cup

mwatercwater(T_f - Ti) + mcopperccopper(T_f - Ti) = mcupccup(Ti - T_f)

Substituting the given values:

(0.38 kg)(4186 J/kg·°C)(T_f - 15°C) + (0.62 kg)(387 J/kg·°C)(T_f - 61°C) = (0.59 kg)(900 J/kg·°C)(15°C - T_f)

Simplifying and solving for T_f, we get T_f ≈ 21.4°C.