What Is Energy? — Question 1

Question 1

Energy accounting begins with a boundary

For this introductory problem use the supplied accounting rule $\Delta E=E_{\mathrm{in}}-E_{\mathrm{out}}$, with all quantities in joules. A sealed device contains a battery and motor. During one operation the battery store decreases by 80 J, a flywheel gains 55 J, and the casing gains 15 J of thermal energy. No other internal store changes.

1. Find the change in total energy of the device.

2. Infer the net energy transfer across its boundary.

3. If the flywheel alone is selected as the system, what is its energy change and why is the answer different?

Question 1 - Solution

Energy accounting begins with a boundary

(a) Add signed changes inside the boundary.

The governing relation is $$\boxed{\Delta E_{\mathrm{system}}=\sum_j\Delta E_j=E_{\mathrm{in}}-E_{\mathrm{out}}}$$

$$\Delta E=-80+55+15=-10\ \mathrm J.$$ The battery loss must not be counted again as a transfer through the outer boundary.

(b) Use the supplied balance.

$$E_{\mathrm{in}}-E_{\mathrm{out}}=-10\ \mathrm J:$$ 10 J leaves on a net basis. The data do not separately fix total incoming and outgoing transfers.

(c) Change the system consistently.

The flywheel has $$\Delta E=+55\ \mathrm J.$$ Its boundary excludes the battery and casing, so energy passed from the motor to the flywheel crosses this smaller boundary. Different systems have different balances.