Question

A sheet of gold weighing 10.0 g and a temperature of 18°C is placed flat on an iron sheet weighing 20.0 g and at a temperature of 55.6°C. What is the final temperature of the combined metals? Assume no heat is lost to the surroundings. Specific heat for gold and iron are 0.129 and 0.444 J/g°C.

a) 34.5°C
b) 38.2°C
c) 42.1°C
d) 45.8°C

Answer 1

To find the final temperature of gold and iron when they are placed together, we use the conservation of energy principle, where the heat gained by gold is equal to the heat lost by iron. By setting up the equation and solving it with the given specific heats and masses, we find the final temperature to be 38.2°C.

Step-by-step explanation:

The question is about the final temperature of two metals, gold and iron, with different initial temperatures being placed together until they reach thermal equilibrium. To solve this, we can use the equation Q = mcΔt, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and Δt is the change in temperature. Since no heat is lost to the surroundings, the heat lost by the hotter iron will equal the heat gained by the colder gold, which can be expressed as:

mgoldcgold(Tfinal - Tinitial,gold) = mironciron(Tinitial,iron - Tfinal)

Inserting the given values and solving for Tfinal we get:

10.0 g * 0.129 J/g°C (Tfinal - 18°C) = 20.0 g * 0.444 J/g°C (55.6°C - Tfinal)

Solve for Tfinal to find the final equilibrium temperature of the two metals, which is 38.2°C (Option b).