Temperature and Heat — Question 8

Question 8

A temperature plateau still admits heat transfer

A pure sample is at its melting temperature with solid and liquid coexisting. In the ideal model its temperature remains fixed while melting requires latent energy $L=200\,\mathrm{kJ/kg}$. Initially it contains .30 kg solid and .20 kg liquid. Heat enters at 50 W; neglect other transfers.

1. Find heat absorbed and solid remaining after 400 s.

2. Find the time at which melting just finishes. Can the subsequent temperature be found from $L$ alone?

Question 8 - Solution

A temperature plateau still admits heat transfer

(a) Method and calculation

$$Q=P t=50(400)=20000\,\mathrm J.$$$$m_{\mathrm{melted}}=Q/L=.100\,\mathrm{kg},\quad m_{\mathrm{solid}}=.300-.100=.200\,\mathrm{kg}.$$Temperature stays at the melting value while both phases remain.

(b) Interpretation and further calculation

$$Q_{\mathrm{finish}}=.300(200000)=60000\,\mathrm J.$$$$t_{\mathrm{finish}}=60000/50=1200\,\mathrm s.$$Afterward one needs the liquid heat capacity, and any relevant loss law, to determine its temperature. The latent-energy parameter does not describe warming of a single phase.

Physical check

$\Delta T=0$ is compatible with $Q>0$ when the phase fraction changes.