The specific heat of ice is 2.10 kJ/kg °C, the heat of fusion for ice at 0 °C is 333.7 kJ/kg, the specific heat of water 4.186 kJ/kg °C, and the heat of vaporization of water at 100 °C is 2,256 kJ/kg. What is the final equilibrium temperature when 10.0 grams of ice at −15.0 °C is mixed with 3.00 grams of steam at 100 °C?

Question

Quizplus · Accepted Answer

To find the final equilibrium temperature when mixing substances at different phases and temperatures, we use the principle of conservation of energy, where the heat lost by the warmer substance equals the heat gained by the cooler substance. Here, we have ice at -15°C and steam at 100°C. The process involves multiple steps for each substance: 1. Heating ice from -15°C to 0°C.2. Melting ice at 0°C to water.3. Heating water from 0°C to the final temperature (Tf).4. Condensing steam at 100°C to water.5. Cooling water from 100°C to Tf.The heat for each step is calculated using the specific heat capacities, heat of fusion, and heat of vaporization given in the problem. The sum of heats for the ice/water must equal the sum of heats for the steam/water in reverse, leading to the final temperature. This problem requires iterative calculation or algebraic solution based on the energy balance equation. The correct answer is found by applying these principles and solving for the final temperature, which is 80.3 °C.

The Specific Heat of Ice Is 2