What will be the equilibrium temperature when a 245 g block of copper at 285 oC
is placed in a 145 g aluminum calorimeter cup containing 825 g of water at 12.0 oC?
add the changes in heat, they have to equal zero.
masscopper*ccu*(Tf-285)+massal*cal*(tf-12)+masswater*cwater*(tf-12)=0
solve for Tf
To find the equilibrium temperature, we need to use the principle of thermal equilibrium:
First, we calculate the heat gained or lost by each component in the system:
1. The block of copper:
- Mass (m1) = 245 g
- Initial temperature (T1) = 285 °C
- Specific heat capacity of copper (c1) = 0.386 J/g°C (provided by reference sources)
- Heat lost by copper (Q1) = m1 * c1 * (T2 - T1), where T2 is the equilibrium temperature. Since the copper is losing heat, we use (T2 - T1).
2. The aluminum calorimeter cup:
- Mass (m2) = 145 g
- Specific heat capacity of aluminum (c2) = 0.897 J/g°C (provided by reference sources)
- Heat gained by the cup (Q2) = m2 * c2 * (T2 - Tcup), where T2 is the equilibrium temperature and Tcup is the initial temperature of the cup.
3. The water:
- Mass (m3) = 825 g
- Initial temperature (T3) = 12.0 °C
- Specific heat capacity of water (c3) = 4.18 J/g°C (provided by reference sources)
- Heat gained by the water (Q3) = m3 * c3 * (T2 - T3), where T2 is the equilibrium temperature.
Now, since the heat lost by the copper is equal to the heat gained by the aluminum cup and water (according to the principle of thermal equilibrium), we can set up an equation:
Q1 = Q2 + Q3
m1 * c1 * (T2 - T1) = m2 * c2 * (T2 - Tcup) + m3 * c3 * (T2 - T3)
Substituting the given values:
245 g * 0.386 J/g°C * (T2 - 285 °C) = 145 g * 0.897 J/g°C * (T2 - Tcup) + 825 g * 4.18 J/g°C * (T2 - 12.0 °C)
Now, we can solve this equation for T2, which will give us the equilibrium temperature.