Calorimetry & MixingJEE Main

Concept

When two bodies at different temperatures touch, heat flows from hot to cold until they reach a common equilibrium temperature. With no losses, the heat lost by the hot body exactly equals the heat gained by the cold one.

Key formula

Derivation

Heat exchanged is $Q = mc\,\Delta T$. Setting heat lost = heat gained and solving for $T_f$ gives the mass-and-specific-heat-weighted average of the two temperatures.

Equal masses of the same substance simply meet in the middle. A larger $mc$ (heat capacity) pulls the final temperature toward that body.

Scenarios to explore

• Calorimetry & Mixing — Final temperature when hot meets cold.

Real-world applications

• Measuring specific heats with a calorimeter.
• Mixing hot and cold water; cooling systems.
• Why coastal climates are mild (water's high specific heat).

JEE exam tips

• Water's huge specific heat (4180 J/kg·K) makes it resist temperature change.
• If a phase change occurs, include $Q = mL$ for the latent heat.
• $T_f$ always lies between $T_1$ and $T_2$ (no losses).

Common mistakes

• Forgetting to convert grams to kilograms (or keeping units consistent).
• Ignoring the calorimeter's own heat capacity in real experiments.
• Using the formula across a phase change without adding latent heat.

Exam traps to avoid

• If one body would cross its melting/boiling point, latent heat must be accounted for.
• Heat capacity $mc$, not mass alone, decides which way $T_f$ leans.