What Is Energy? — Question 2

Question 2

A zero choice cannot alter an energy change

Two analysts assign energies to three states of the same system. Their conventions may differ by one constant offset. The records are below; the system makes the cycle A to B to C to A.

1. Determine whether one constant offset relates the records.

2. Find each energy change in the cycle under both conventions.

3. A third analyst changes only the B entry of record II to 140 J. Can a new constant offset repair the whole record?

Question 2 - Solution

A zero choice cannot alter an energy change

(a) Compare corresponding states.

The governing relation is $$\boxed{E_{\mathrm{II}}(s)=E_{\mathrm{I}}(s)+C\quad\Longrightarrow\quad\Delta E_{\mathrm{II}}=\Delta E_{\mathrm{I}}}$$ The offset is identical in every state: $$110-10=135-35=120-20=100\ \mathrm J.$$ Thus $E_{\mathrm{II}}=E_{\mathrm{I}}+100\ \mathrm J$.

(b) Subtract endpoints, not reference levels.

Subtract endpoint values in either record: $$\Delta E_{AB}=35-10=25\ \mathrm J,\quad\Delta E_{BC}=20-35=-15\ \mathrm J.$$ $$\Delta E_{CA}=10-20=-10\ \mathrm J,\qquad\sum_{\mathrm{cycle}}\Delta E=25-15-10=0.$$

(c) Require the same offset everywhere.

The proposed replacement is inconsistent with a common zero shift: $$C_B=140-35=105\ \mathrm J\ne C_A=C_C=100\ \mathrm J.$$ It changes energy differences and cannot be absorbed into one additive constant.