Physics 5054/21 — October/November 2011

Walkthrough

The thermal energy required to change the state of a substance without changing its temperature is given by $Q = ml$, where $m$ is the mass and $l$ is the specific latent heat. Substitute the unrounded mass ($0.05888\text{ kg}$) and the given specific latent heat of fusion for ice ($3.4 \times 10^5\text{ J/kg}$): $Q = 0.05888 \times 3.4 \times 10^5 = 20019.2\text{ J}$. Expressing this in standard form to two significant figures gives $2.0 \times 10^4\text{ J}$. Note that using the rounded mass ($0.059\text{ kg}$) gives $20060\text{ J}$, which is also accepted as $2.01 \times 10^4\text{ J}$ or $2.0 \times 10^4\text{ J}$.

Key Takeaways

Specific latent heat is the energy needed to change the state of $1\text{ kg}$ of a substance. The formula $Q = ml$ applies to melting (fusion) or boiling (vaporisation). During a change of state, the temperature remains constant while thermal energy is used to break intermolecular bonds.

Common Mistakes

Using the wrong formula (e.g. $Q = mc\Delta\theta$, which is for temperature changes, not state changes). Forgetting to convert the latent heat from $\text{J/kg}$ correctly or misplacing the decimal point in scientific notation. Rounding the mass too early and getting a slightly different final answer.

Things to Be Careful About

The question asks for the energy absorbed as the ice melts at $0^\circ\text{C}$. Since there is no temperature change, only the latent heat formula is used. Ensure the final answer is given in joules (J) and to an appropriate number of significant figures (2 or 3).