Worked exercise — A cup of coffee

Problem

How much heat is needed to bring $200$ g of water from $20\ ^{\circ}$C to $95\ ^{\circ}$C? And how many minutes does that correspond to on a $1.5$ kW induction hob?

Solution

Setting up. The heat to warm the water is $Q=m\,c\,\Delta T$, with $c=4186\ \mathrm{J/(kg\cdot K)}$ and $\Delta T=95-20=75\ \mathrm{K}$. Substitution: $Q=0.2\cdot 4186\cdot 75\approx 6.28\cdot10^{4}\ \mathrm{J}\approx 63\ \mathrm{kJ}$ Time at constant power $P=1500\ \mathrm{W}$, from $t=Q/P$: $t=\frac{63000}{1500}=42\ \mathrm{s}$ $\ev{Q\approx 63\ \mathrm{kJ},\quad t\approx 42\ \mathrm{s}}$ The time is ideal: it neglects the kettle’s losses. In practice it takes 1.5–2 minutes.

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Topics: Termologia Concepts: Calore specifico e capacità termica