Balance Heat Gained Against Heat Lost, Step by Step
Calorimetry problems are all the same bookkeeping: heat lost by the hot bodies equals heat gained by the cold ones, provided you stop at the right phase change. The one skill is deciding step by step whether the ice melts completely, the steam condenses completely, or the mixture stalls at 0 °C or 100 °C.
Chemistry questions first require the material, particles or reaction condition to be identified before a formula or rule is selected.
Heat formulas and constants
Taking 1 g of ice at 0 °C all the way to steam at 100 °C needs 80 (melting) + 100 (warming) + 540 (boiling) = 720 cal. On a heating curve the flat segments are phase changes, where all the heat goes into latent heat and the temperature stays fixed, and the sloped segments are warming of a single phase; the length of a flat segment divided by the heating rate gives m L.
Mixing: test the end states before solving
Mix 1 kg of ice at -10 °C with 4.4 kg of water at 30 °C. Warming the ice to 0 °C takes 1000 x 0.5 x 10 = 5000 cal and melting it takes 80 000 cal, a total of 85 000 cal, while cooling the water to 0 °C releases 4400 x 30 = 132 000 cal. Because 132 000 is more than 85 000, all the ice melts and the final temperature is above 0 °C;
In the same way, for steam added to water or ice added to water at other temperatures, compare the heat available at each phase boundary before assuming a final temperature.
Heat capacity that rises with temperature
If the heat capacity of a material increases with temperature, a hot body and an identical cold body placed in contact do not meet at the simple average. The hotter body has the larger heat capacity, so it cools by a smaller number of degrees than the colder body warms for the same heat transfer, and the final temperature is above the average (here, above 50 °C).
Mechanical energy that ends up as heat
When a bullet is stopped by an ice block, or a piece of ice falls and melts, kinetic or potential energy becomes heat. Write energy conservation first: usable heat = efficiency x (kinetic energy or mgh), then equate it to m L for the mass melted or to m s ΔT for a temperature rise.
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- ✓Q = m s ΔT for warming and Q = m L for a phase change; the temperature stays constant during a phase change
- ✓Water: s = 1 cal/g°C, ice: s = 0.5 cal/g°C, L(fusion) = 80 cal/g, L(vaporisation) = 540 cal/g
- ✓Before solving a mixing problem, compare the heat released by the hot body at each phase boundary with the heat the cold body can absorb
- ✓A material whose heat capacity rises with temperature gives a final temperature above the simple average when hot and cold bodies touch
- ✓For energy-to-heat problems, apply the stated efficiency to mgh or (1/2)mv² before using m L or m s ΔT
Do not set heat lost equal to heat gained with an assumed final temperature before checking the phase boundaries. If the ice does not melt completely, or the steam does not condense completely, the mixture sits at 0 °C or 100 °C and the equation you wrote is for the wrong final state.
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