Work, Energy, and Emf — Question 1

Question 1

Chemical power exceeds terminal power during discharge

A battery has emf $\mathcal E=18.0$ V and internal resistance r=.400 ohm. It delivers current I=3.00 A from its positive terminal for 40.0 s. Treat its parameters as constant.

1. Find terminal voltage, chemical power and internal heating power.

2. Find the delivered energy and verify the full energy balance.

Question 1 - Solution

Chemical power exceeds terminal power during discharge

(a) Method and calculation

$$V=\mathcal E-Ir=18.0-3(.400)=16.8\,\mathrm V.$$$$P_{\mathrm{chem}}=\mathcal EI=54.0\,\mathrm W,\quad P_r=I^2r=3.60\,\mathrm W.$$

(b) Interpretation and further calculation

$$W_{\mathrm{out}}=VIt=(16.8)(3)(40)=2016\,\mathrm J.$$$$W_{\mathrm{chem}}=2160\,\mathrm J=W_{\mathrm{out}}+I^2rt=2016+144.$$

Physical check

Internal resistance converts some chemical energy into heat before it reaches the external load.