Heat Transfer Calculations: A Chemistry Guide with Examples

📚 Quick Study Guide

• 🔥 Heat (q): Energy transferred between objects or systems due to a temperature difference. Measured in Joules (J).
• 🌡️ Temperature (T): A measure of the average kinetic energy of the particles in a substance. Measured in Celsius (°C) or Kelvin (K).
• ⚖️ Specific Heat Capacity (c): The amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius (or 1 Kelvin). Units: J/g°C or J/gK.
• 🧊 Heat Transfer Equation: $q = mc\Delta T$, where:
  • $q$ = heat transferred
  • $m$ = mass of the substance
  • $c$ = specific heat capacity
  • $\Delta T$ = change in temperature ($T_{final} - T_{initial}$)
• ➡️ Heat Transfer in Phase Changes: During phase changes (e.g., melting, boiling), temperature remains constant. Use these equations:
  • Melting/Freezing: $q = m \cdot \Delta H_{fus}$, where $\Delta H_{fus}$ is the enthalpy of fusion.
  • Boiling/Condensation: $q = m \cdot \Delta H_{vap}$, where $\Delta H_{vap}$ is the enthalpy of vaporization.
• 📏 Units are Key: Ensure all units are consistent before performing calculations. Convert grams to kilograms or Celsius to Kelvin if necessary.

🧪 Practice Quiz

1. A 50.0 g piece of metal at 85.0°C is placed in 100.0 g of water at 22.0°C. The final temperature of the water and metal is 25.6°C. Assuming no heat is lost to the surroundings, what is the specific heat capacity ($c$) of the metal?
   1. 0.128 J/g°C
   2. 0.385 J/g°C
   3. 0.449 J/g°C
   4. 0.900 J/g°C
2. How much heat is required to raise the temperature of 25.0 g of water from 20.0°C to 80.0°C? (Specific heat capacity of water = 4.184 J/g°C)
   1. 209.2 J
   2. 2092 J
   3. 6276 J
   4. 8368 J
3. What is the final temperature when 100.0 g of water at 25.0°C is mixed with 50.0 g of water at 60.0°C? Assume no heat loss to the surroundings.
   1. 30.0°C
   2. 36.7°C
   3. 42.5°C
   4. 45.0°C
4. Calculate the amount of heat needed to melt 10.0 g of ice at 0°C. ($\Delta H_{fus}$ of ice = 334 J/g)
   1. 33.4 J
   2. 334 J
   3. 3340 J
   4. 33400 J
5. What mass of water can be heated from 25.0°C to 50.0°C by the addition of 5000 J of heat? (Specific heat capacity of water = 4.184 J/g°C)
   1. 23.9 g
   2. 47.8 g
   3. 119.5 g
   4. 209.2 g
6. If 50 g of a substance absorbs 2000 J of heat and its temperature increases by 20°C, what is the specific heat capacity of the substance?
   1. 2 J/g°C
   2. 4 J/g°C
   3. 5 J/g°C
   4. 25 J/g°C
7. Determine the heat required to vaporize 25 g of water at 100°C. The enthalpy of vaporization of water is 2260 J/g.
   1. 56.5 kJ
   2. 565 kJ
   3. 90.4 kJ
   4. 904 kJ