Concept:The first law of thermodynamics requires accounting for the work done when a system changes volume, even during phase changes like melting.
Formula:$$ \Delta E = q - P\Delta V $$
Solution:- Heat absorbed (\( q \)) = \( +6025 \text{ J} \).
- Change in volume (\( \Delta V \)) = \( V_{\text{water(liquid)}} - V_{\text{ice(solid)}} \).
\( \Delta V = 0.018 - 0.020 = -0.002 \text{ dm}^3 \) (Water uniquely shrinks when melting).
- Calculate Work (\( W = P\Delta V \)) in Joules:
\( W = 1 \text{ atm} \times -0.002 \text{ dm}^3 = -0.002 \text{ atm.dm}^3 \).
Convert to Joules: \( -0.002 \times 101.33 = -0.2026 \text{ J} \).
- Calculate Internal Energy:\( \Delta E = 6025 - (-0.2026) = 6025.2026 \text{ J} \).
- Rounded to two decimal places, this matches exactly \( 6025.20 \text{ J} \).
Why other options are incorrect:Other options result from incorrectly adding the volume change as expansion (which would subtract work) or ignoring the contraction physics entirely.
Quality & Fidelity Assurance:
Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.