SUMMARY
The final temperature of a system consisting of a 10 kg piece of zinc at 68°C and 32 kg of water at 14°C can be calculated using the principle of conservation of energy. The specific heats of zinc and water are 388 J/kg·°C and 4180 J/kg·°C, respectively. By setting the energy gained by water equal to the energy lost by zinc, the equation (10 kg)(388 J/kg·°C)(Tf - 68°C) + (32 kg)(4180 J/kg·°C)(Tf - 14°C) = 0 can be solved for the final temperature Tf. The calculations lead to a final temperature of approximately 41°C.
PREREQUISITES
- Understanding of thermal equilibrium and heat transfer principles
- Knowledge of specific heat capacity and its application in thermal calculations
- Ability to manipulate algebraic equations to solve for unknowns
- Familiarity with units of measurement in physics (e.g., kg, °C, J)
NEXT STEPS
- Study the laws of thermodynamics, particularly the first law regarding energy conservation
- Learn about specific heat capacity and its role in different materials
- Explore more complex heat transfer problems involving phase changes
- Practice solving thermal equilibrium problems with varying masses and temperatures
USEFUL FOR
Students studying physics, particularly those focusing on thermodynamics, as well as educators looking for practical examples of heat transfer and energy conservation in real-world scenarios.