Question

A scientist whose scale is broken but who has a working

2.5 kW heating coil and a thermometer decides to improvise

to determine the mass of a block of aluminum she has recently

acquired. She heats the aluminum for 30 s and finds that its

temperature increases from 20C to 35C. What is the mass of the

aluminum?

Short answer

The mass of the aluminum is$m=5.643[\mathrm{kg}]$

Step-by-step solution

Given information

The coil's power is$2.5\mathrm{kW}$, it runs for $30$seconds, and the temperature increment is${15}^{0}c$It's an aluminium block.

Calculation

formula used:

The heat provided by the heating coil is:

$Q=P\Delta t$

From aluminum property table:

$C_p=0.886\left[\frac{J}{g\Delta °C}\right]$

The heating coil was turned on 30 seconds, and the heat produced is:

$$\begin{gathered} Q=2.5\left[kW\right]\Delta 30\left[s\right]=75\left[kJ\right]=75,000\left[J\right] \\ Q=m\Delta 0.886\left[\frac{J}{g\Delta °C}\right]\Delta \left(35\left[{}^{\circ }\mathrm{C}\right]-20\left[{}^{\circ }\mathrm{C}\right]\right)=75,000\left[J\right] \end{gathered}$$

Solving for $m$:

$$\begin{gathered} m=\frac{75,000\left[J\right]}{\left.\left.0.886\left[\frac{J}{8\Delta °\mathrm{C}}\right]\Delta \left(35{}^{\circ }\mathrm{C}\right]-20{}^{\circ }\mathrm{C}\right]\right)} \\ =5,643[\mathrm{g}]m \\ =5.643[\mathrm{kg}] \end{gathered}$$

We could compute the block's mass by supposing it absorbed all of the heat. This isn't always the case, and the mass will be smaller.