Overview
This lecture focuses on practicing the rearrangement of equations, specifically using the heat equation to solve for the final temperature after a substance absorbs energy.
Understanding the Heat Equation
- The heat equation is Q = MCΔT, where Q is heat, M is mass, C is specific heat, and ΔT is temperature change.
- ΔT represents (T_final - T_initial).
Rearranging the Equation
- To solve for T_final, first divide both sides by MC: Q / (MC) = T_final - T_initial.
- Add T_initial to both sides to isolate T_final: T_final = T_initial + Q / (MC).
Problem Example Setup
- Given values: Q = 840 J, M = 10 g, T_initial = 25°C, C = 4.184 J/g°C.
- Substitute the values into the rearranged equation:
T_final = 25 + (840) / (10 × 4.184).
Calculations and Units
- Calculate the denominator: 10 × 4.184 = 41.84.
- Divide: 840 / 41.84 ≈ 20.07.
- Add to initial temperature: 25 + 20.07 ≈ 45.07°C.
- Check units: Joules, grams cancel properly; degrees Celsius remains.
- Use correct significant figures: Answer should have two significant figures (from 840 J), so T_final = 45°C.
Key Terms & Definitions
- Q (Heat) — the amount of thermal energy absorbed or released (in joules).
- M (Mass) — the mass of the substance (in grams).
- C (Specific Heat) — the energy required to change 1 gram of a substance by 1°C (J/g°C).
- ΔT (Change in Temperature) — the difference between final and initial temperatures (T_final - T_initial).
Action Items / Next Steps
- Practice rearranging similar equations for different variables.
- Ensure calculation steps use correct units and significant figures.