A sheet of gold of mass 100g and a teperature of 18.0 degrees is placed flat on a sheet of iron weighing 20g and at a temperature of 55.6 degrees. what is the final temperature of the combined metal.
heat lost by Fe + heat gained by Au = 0
[mass Fe x specific heat Fe x (Tfinal-Tinitial)] + [mass Au x specific heat Au x (Tfinal-Tinitial)] = 0
Solve for Tfinal.
To determine the final temperature of the combined metals, we can use the principle of thermal equilibrium, which states that when two objects are in contact, they will eventually reach the same temperature.
To solve this problem, we need to consider the heat gained or lost by each metal and equate them. The equation for heat transfer is:
Q = m * c * ΔT
Where:
Q is the heat transferred
m is the mass of the object
c is the specific heat capacity of the material
ΔT is the change in temperature
For gold:
m1 = 100 grams
c1 = specific heat capacity of gold (0.128 J/g°C)
ΔT1 = final temperature - initial temperature
For iron:
m2 = 20 grams
c2 = specific heat capacity of iron (0.449 J/g°C)
ΔT2 = final temperature - initial temperature
Since the two metals will reach the same temperature, we can equate the heat transferred by gold to the heat transferred by iron:
m1 * c1 * ΔT1 = m2 * c2 * ΔT2
Now, let's substitute the given values into the equation:
(100 g) * (0.128 J/g°C) * (final temperature - 18.0°C) = (20 g) * (0.449 J/g°C) * (55.6°C - final temperature)
Simplifying the equation:
12.8 * (final temperature - 18.0) = 8.98 * (55.6 - final temperature)
Solving for the final temperature:
12.8 * final temperature - 230.4 = 8.98 * 55.6 - 8.98 * final temperature
12.8 * final temperature + 8.98 * final temperature = 8.98 * 55.6 + 230.4
21.78 * final temperature = 503.688 + 230.4
21.78 * final temperature = 734.088
final temperature = 734.088 / 21.78
final temperature ≈ 33.68°C
Therefore, the final temperature of the combined metals is approximately 33.68°C.