Thermal Energy and Phase Changes Quiz

Concept: phase change priority at a melting point. Ice at 0°C cannot warm above 0°C until it has melted because added energy first goes into the phase change.

Concept: latent heat of fusion. Melting at constant temperature uses q=ml_f. l_f is the energy per kilogram required to change ice to liquid water at 0°C.

Concept: applying q=ml_f. Multiply mass by latent heat of fusion. q=0.030×334,000=10,020 j, which is the energy required for complete melting at 0°C.

Concept: coexistence of phases fixes temperature. When ice and water coexist at equilibrium (at 1 atm), the temperature remains at 0°C.

Concept: sensible heat release magnitude and sign. The magnitude is q=mc|Δt|=0.25×4180×20=20,900 j.

Concept: multi-stage energy balance with phase change. You must compare heat available from cooling water with heat required to melt ice.

Concept: mixing same substance. Use a mass-weighted average. t_f=(0.40(30)+0.10(10))/0.50=26°C.

Concept: heat capacity (mc) determines influence. A larger mass has a larger heat capacity, so it stores more thermal energy per degree of temperature change.

Concept: heat gained by water. The water warms by Δt=24−20=4°C, so q=mcΔt=0.30×4180×4=5,016 j.

Concept: equal and opposite heat changes. In an insulated exchange, heat gained by water equals heat lost by the metal.

Concept: error propagation in c=|q|/(m|Δt|). Recording t_i too high makes the calculated |Δt| too large.

Concept: non-isolated systems. If heat leaks to the surroundings, then not all the heat lost by the hot object ends up in the cold object.

Concept: temperature change sign. Δt is defined as final minus initial. Cooling makes t_f<t_i so Δt is negative.

Concept: applying q=mcΔt for warming. Here Δt=23−18=5°C. q=0.20×4180×5=4,180 j.

Concept: equilibrium bounds in mixing. Without external energy, the mixture cannot end up hotter than the hottest part or colder than the coldest part.

Concept: comparing transferred heat to melting requirement. Since the transferred heat exactly matches the value needed to melt all the ice, it melts completely.

Concept: solving for latent heat. Use l_f=q/m for a melting process at constant temperature.

Concept: specific heat from q, m, and Δt. Use c=|q|/(m|Δt|). c=2400/(0.30×20)=400 j/(kg·°C).

Concept: reasons real results are lower than ideal. Heat loss to air, heat absorbed by the cup, and cooling during transfer all reduce the energy that actually warms the water.

Concept: stage-based problem solving. Calorimetry often involves different physical processes, each with its own equation.