Answer :
The final temperature when the two objects reach thermal equilibrium is approximately 195.49°C.
To find the final temperature when the two objects reach thermal equilibrium, you can use the principle of conservation of energy and the specific heat capacities of the materials.
The principle of conservation of energy states that the total energy of an isolated system remains constant. In this case, the energy transferred from the hot copper object will be equal to the energy gained by the cold aluminum object. This can be expressed as:
m₁ x c₁ x( final temperature - T₁) = m₂ x c₂ x ( final temperature - T₂)
Where; m₁ = mass of the copper object = 9.89 kg
m₂ = mass of the aluminum object = 2.45 kg
c₁ = specific heat capacity of copper ≈ 0.385 J/(g°C) or 385 J/(kg°C)
c₂ = specific heat capacity of aluminum ≈ 0.897 J/(g°C) or 897 J/(kg°C)
T₁ = initial temperature of copper = 98.2°C
T₂ = initial temperature of aluminum = 26.1°C
[tex]T_{f}[/tex] = final temperature when they reach thermal equilibrium (what we want to find)
Now, plug in these values and solve for [tex]T_{f}[/tex]
9.89 kg x 385J/ (kg °C) x (final temperature - 98.2°C) = 2.45kg X 897J / (kg°C) x (final temperature - 26.1°C)
Now, solve for final temperature;
9.89 x 385 x (final temperature - 98.2°C) = 2.45 X 897 x (final temperature - 26.1°C)
3816.65 x (final temperature - 98.2°C) = 2200.65 x (final temperature - 26.1°C)
Now, expand and solve for final temperature;
3816.65 x [tex]T_{f}[/tex] - 3816.65 x 98.2 = 2200.65 x [tex]T_{f}[/tex] - 2200.65 x 26.1
3816.65 x[tex]T_{f}[/tex] - 2200.65 x [tex]T_{f}[/tex] = 3816.65 x 98.2 - 2200.65 x 26.1
1616 x [tex]T_{f}[/tex] = 374536.13 - 57513.66
1616 x [tex]T_{f}[/tex] = 316022.47
Now, divide by 1616 to find [tex]T_{f}[/tex];
[tex]T_{f}[/tex] = 316022.47/1616 ≈ 195.49°C
So, the final temperature when the two objects reach thermal equilibrium is approximately 195.49°C.
To know more about thermal equilibrium here
https://brainly.com/question/3127033
#SPJ4
