60.0 g of iron that has an initial temperature of 250 degrees C and 60.0 g of gold that has an initial temperature of 45.0 degrees C are brought into contact with one another. Assuming no heat is lost to the surroundings, what will be the temperature when two metals reach thermal equilibrium? The specific heat capacity of iron = 0.449 J/g* degrees C and gold = 0.128 J/g* degrees C.
sph = specific heat
heat lost by Fe + heat gained by Au = 0
[mass Fe x sph Fe x (Tfinal-Tinitial)] + [mass Au x sph Au x (Tfinal-Tinitial)] = 0
Solve for Tfinal
204.52 *C
To solve this problem, we will use the principle of thermal equilibrium, which states that when two objects with different temperatures come into contact, they will eventually reach a common temperature.
First, let's calculate the heat lost or gained by each metal:
Heat lost or gained by iron (Q_iron) = mass of iron (m_iron) x specific heat capacity of iron (c_iron) x change in temperature of iron (ΔT_iron)
Q_iron = 60.0 g x 0.449 J/g*°C x (final temperature - 250°C)
Heat lost or gained by gold (Q_gold) = mass of gold (m_gold) x specific heat capacity of gold (c_gold) x change in temperature of gold (ΔT_gold)
Q_gold = 60.0 g x 0.128 J/g*°C x (final temperature - 45.0°C)
Since the system is isolated, the heat lost by iron is equal to the heat gained by gold:
Q_iron = -Q_gold
Substituting the expressions for Q_iron and Q_gold:
60.0 g x 0.449 J/g*°C x (final temperature - 250°C) = -60.0 g x 0.128 J/g*°C x (final temperature - 45.0°C)
Simplifying:
0.449 J*°C x (final temperature - 250°C) = -0.128 J*°C x (final temperature - 45.0°C)
Now, let's solve for the final temperature:
0.449 final temperature - 0.449 x 250 = -0.128 final temperature + 0.128 x 45.0
0.449 final temperature + 0.128 final temperature = 0.128 x 45.0 + 0.449 x 250
0.577 final temperature = 5.76 + 112.25
0.577 final temperature = 118.01
final temperature = 118.01 / 0.577
final temperature ≈ 204.42°C
Therefore, the final temperature when the two metals reach thermal equilibrium is approximately 204.42°C.