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Question

A portable coffee heater supplies a potential difference of 12.0 V across a Nichrome heating element with a resistance of $2.00 \Omega$. How many minutes would it take to heat 1.00 kg of coffee from $20.0^{\circ} \mathrm{C}$ to $50.0^{\circ} \mathrm{C}$ with this heater? Coffee has a specific heat of $4184 \mathrm{J} /\left(\mathrm{kg} \cdot^{\circ} \mathrm{C}\right)$. Neglect any energy losses to the environment.

Solution

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1 of 2The time needed to heat up this amount of coffe is equal to energy required divided by the power:

$\begin{gather*} \Delta t=\dfrac{\Delta E}{P}=\dfrac{c_vm\Delta T}{P}=\dfrac{(1)(4184)(30)}{72}\approx \boxed{1743\mathrm{~s}\approx 29\mathrm{~min}} \end{gather*}$

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