Question

An 8 g sheet of gold with a temperature of 15 ֯C is laid flat on a sheet of iron that weighs 18 g and has a temperature of 40 ֯C. Given that the specific heat capacities of Au and Fe are 0.129 J g-1 ֯C-1 and 0.444 J g-1 ֯C-1, respectively, what is the final temperature of the combine metals? Assume that no heat is lost to the surrounding, and the heat gained by the gold is equal to the heat lost by iron.

Answer 1

The final temperature of the combined gold and iron will be approximately 33.5°C.

Step-by-step explanation:

To find the final temperature of the combined metals, we can use the equation:

heat gained by gold = heat lost by iron

The heat gained by the gold can be calculated using the equation:

heat = mass x specific heat capacity x temperature change

The heat lost by the iron can be calculated using the same equation. Setting these two equations equal to each other and solving for the final temperature will give us the answer.

Using the given values:

1. Mass of gold = 8 g
2. Temperature of gold = 15 °C
3. Specific heat capacity of gold = 0.129 J/g °C
4. Mass of iron = 18 g
5. Temperature of iron = 40 °C
6. Specific heat capacity of iron = 0.444 J/g °C

We can calculate the heat gained by the gold and the heat lost by the iron:

heat gained by gold = 8 g x 0.129 J/g °C x (final temperature - 15 °C)

heat lost by iron = 18 g x 0.444 J/g °C x (40 °C - final temperature)

Setting these two equations equal to each other:

8 g x 0.129 J/g °C x (final temperature - 15 °C) = 18 g x 0.444 J/g °C x (40 °C - final temperature)

Simplifying the equation, we can solve for the final temperature:

1.032(final temperature - 15) = 8.232(40 - final temperature)

1.032final temperature - 15.48 = 329.28 - 8.232final temperature

9.264final temperature + 1.032final temperature = 329.28 + 15.48

10.296final temperature = 344.76

final temperature = 344.76 / 10.296

final temperature ≈ 33.5 °C