Calorimetry: Specific Heat, Latent Heat and Phase Change Calculations

Calorimetry measures heat by watching temperature change. Two equations cover almost every question: one for heating a substance, one for changing its phase. Add conservation of energy and you can solve any mixing problem.

Core formulas

c is specific heat and L is latent heat of fusion or vaporization. Heat flows from the hotter object to the colder one until temperatures match.

Heating curve

On a plot of temperature against heat added, slopes are single phases and flat sections are phase changes. On a slope use mcΔT. On a flat section the temperature does not change because the heat goes into breaking intermolecular attractions, so use mL. The vaporization plateau is much longer than the fusion plateau because L_v is larger than L_f.

Worked example

Find the final temperature when 100 g of water at 80 C is mixed with 100 g of water at 20 C.

• Equal masses and equal c, so the final temperature is the average, 50 C.
• For unequal masses: m₁c(80 - T) = m₂c(T - 20), and c cancels.
• Heat needed to melt 10 g of ice at 0 C (L_f = 334 J/g): q = 10 x 334 = 3340 J, with no temperature rise.

Common traps

• Using mcΔT during a phase change. The temperature is flat, so use mL.
• Mixing signs. Set heat lost equal to heat gained with positive magnitudes.
• Mixing units of J and cal, or K and C. A change of 1 K equals a change of 1 C.
• Thinking high specific heat means heating fast. It means slow temperature change.

One-minute recap

q = mcΔT on slopes, q = mL on plateaus. Heat lost equals heat gained. Water has a high specific heat, so it resists temperature change. Vaporization needs more heat than fusion.