Overview
This lecture introduces the concept of specific heat, explains how to calculate the energy required to change the temperature of substances within a phase, and demonstrates using the heat equation to solve relevant problems.
Phase Changes vs. Heating Within a Phase
- Changing phase (solid↔liquid, liquid↔gas) for water requires fixed energy per gram: 80 cal/g (solid to liquid), 540 cal/g (liquid to gas).
- Heating within a single phase involves raising the temperature without a phase change.
Specific Heat and Its Significance
- Specific heat is the energy required to raise 1 gram of a substance by 1°C.
- Substances with low specific heat (e.g., asphalt) heat up more quickly than those with high specific heat (e.g., water).
- For water, specific heat = 1.00 cal/g°C or 4.184 J/g°C.
The Heat Equation
- The heat equation relates energy, mass, specific heat, and temperature change:
Heat (q) = mass (m) × specific heat (SH) × ΔT (change in temperature).
- ΔT (delta T) = final temperature (Tf) - initial temperature (Ti).
- Energy and heat are treated as the same in this course.
Solving Heat Equation Problems
- Always write the equation before solving a problem.
- Use the correct specific heat value for each substance.
- Example: To heat 18g water from 15°C to 25°C:
q = 18g × 1 cal/g°C × (25°C - 15°C) = 180 cal.
- Units cancel to leave energy (e.g., calories or joules).
- Significant figures: count for mass and specific heat, ignore for temperature.
Handling Cooling and Negative Values
- If cooling, ΔT will be negative; negative heat means loss of energy.
- It's acceptable to have negative values for ΔT and q.
Additional Problem-Solving Tips
- To find mass: rearrange heat equation as mass = heat / (specific heat × ΔT).
- Use scientific notation to report answers with correct significant figures when necessary.
Key Terms & Definitions
- Specific Heat (SH) — energy needed to raise 1g of a substance by 1°C.
- Delta T (ΔT) — change in temperature, calculated as Tf - Ti.
- Heat Equation — q = m × SH × ΔT; calculates energy for temperature changes.
- Calorie (cal) — amount of energy to raise 1g water by 1°C.
- Joule (J) — SI unit of energy; 1 cal = 4.184 J.
Action Items / Next Steps
- Memorize the specific heat values for water (1.00 cal/g°C and 4.184 J/g°C).
- Practice solving heat equation problems and always include units at each step.
- Ensure you use the correct number of significant figures and scientific notation where required.