SUMMARY
The discussion addresses calculating the final temperature of a thermally insulated cup containing 0.25 kg of water at 75 °C after adding 0.35 kg of water at 20 °C. The specific heat capacity of water is 4180 J/kg·K. The correct approach uses the principle of conservation of thermal energy, applying the formula T_final = (m1·T1 + m2·T2) / (m1 + m2), resulting in a final temperature closer to the cooler water due to its greater mass. The initial incorrect method involved using mass ratios without applying the heat capacity formula, leading to an inaccurate estimate of approximately 40 °C. The discussion confirms no heat loss to the environment and references engineeringtoolbox.com for validated formulas.
PREREQUISITES
- Thermal energy conservation principles
- Specific heat capacity of water (4180 J/kg·K)
- Mass-weighted temperature averaging formula for mixing fluids
- Basic algebraic manipulation of thermodynamic equations
NEXT STEPS
- Study the formula for final temperature in mixing fluids: T_final = (m1·T1 + m2·T2) / (m1 + m2)
- Explore heat transfer concepts in insulated systems
- Review specific heat capacities for different substances
- Practice thermodynamics problems involving energy conservation and temperature calculations
USEFUL FOR
Students and professionals in thermodynamics, mechanical and chemical engineering, educators teaching heat transfer concepts, and anyone needing to calculate temperature changes in mixed fluids under insulated conditions.
