Thermal Energy and Calorimetry

Heat Transfer and Phase Changes

Calorimetry is the study of heat transfer between substances, especially during phase changes such as melting, freezing, and vaporization. In thermally insulated systems, the principle of conservation of energy applies: the total heat gained by some parts of the system equals the total heat lost by others.

• Heat (Q): The energy transferred due to temperature difference, measured in joules (J) or calories (cal).

• Specific Heat Capacity (c): The amount of heat required to raise the temperature of 1 gram of a substance by 1°C. For water, .

• Latent Heat: The energy required for a substance to change phase at constant temperature.

  • Latent Heat of Fusion (): Energy to melt 1 g of ice at 0°C to water at 0°C.

  • Latent Heat of Vaporization (): Energy to convert 1 g of water at 100°C to steam at 100°C.

Key Equations

• Heat for temperature change: where is mass, is specific heat, and is temperature change.

• Heat for phase change: where is the latent heat (fusion or vaporization).

Example 1: Mixing Steam and Ice

Question: What mass of steam initially at 100°C should be mixed with 160 g of ice at 0°C in a thermally insulated container to produce liquid water at 40°C?

• Process:

  1. Steam at 100°C condenses to water at 100°C (releases ).

  2. Condensed water cools from 100°C to 40°C (releases ).

  3. Ice at 0°C melts to water at 0°C (absorbs ).

  4. Melted water warms from 0°C to 40°C (absorbs ).

• Energy Conservation: Total heat released by steam = Total heat absorbed by ice.

• Application: This type of calculation is common in calorimetry problems involving mixtures and phase changes.

Example 2: Mixing Ice and Water

Question: Ice at 0°C is mixed with 100 g of water at 70°C. What is the final temperature of the mixture?

• Process:

  1. Ice at 0°C absorbs heat to melt (requires ).

  2. Melted water (from ice) and original water exchange heat until thermal equilibrium is reached.

• Energy Conservation: Heat lost by warm water = Heat gained by ice (to melt and then warm up, if any heat remains).

• Application: Used to determine final temperature or phase composition after mixing substances at different temperatures.

Table: Common Values for Water

Summary of Steps for Calorimetry Problems

1. Identify all phase changes and temperature changes.

2. Write energy balance equations using and .

3. Set total heat gained equal to total heat lost (for insulated systems).

4. Solve for the unknown (mass, temperature, etc.).

Example: Mixing steam and ice to produce water at a specific temperature is a classic calorimetry problem, requiring careful accounting of all energy transfers. Example: Determining the final temperature after mixing ice and warm water involves calculating whether all the ice melts and how much the temperature changes. Additional info: These problems are fundamental in introductory physics courses covering thermodynamics and energy conservation.