Budget Input Scale Source Scan - Biophysical Energy Transduction and Molecular Motors Step by Step

Scaling input, useful work, and waste together separates budget size from efficiency. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Thirty input joules split as eighteen plus twelve

This budget keeps efficiency fixed at three fifths. With input 30 joules, useful work is 18 joules and waste heat is 12 joules.

\frac{18}{30}=\frac{3}{5}

Sixty input joules doubles both outputs

Doubling input to 60 joules doubles useful work to 36 joules and waste heat to 24 joules. The fraction stays three fifths.

\frac{36}{60}=\frac{3}{5}

Ninety input joules keeps the same ratio at a larger scale

At input 90 joules, useful work is 54 joules and waste heat is 36 joules. More energy passes through the ledger, but the ratio remains three fifths.

\frac{54}{90}=\frac{3}{5}