Stem-Master
Physics / Chapter 7: Kinetic Energy and Work / Section 7-1

What Is Energy? — Question 8

Section 7-1 · Physics pages 866–867

Question 8 Usable output is not the same as total energy For this introductory problem use the supplied accounting rule ∆E = Ein −Eout, with all quantities in joules. Converter A receives 200 J and delivers 120 J to a desired output; 80 J goes to thermal surroundings. Converter B receives 300 J, delivers 150 J to the desired output, and releases 150 J thermally. Neither changes its stored energy. Define the useful fraction as useful output divided by input. A: input 200 J B: input 300 J useful 120 J thermal 80 J useful 150 J thermal 150 J Each converter divides its input into useful and thermal transfers. (a) Find each useful fraction and compare useful output amounts. (b) Which converter wastes a smaller fraction under this definition? (c) Does the thermal output mean energy has been destroyed? Identify the system for which it is an outgoing transfer.
Show solutionHide solution
Question 8 - Solution Usable output is not the same as total energy A: input 200 J B: input 300 J useful 120 J thermal 80 J useful 150 J thermal 150 J (a) Separate a fraction from an amount. The governing relation is η = Euseful Einput , fthermal = 1 −η A has 120/200 = 0.60; B has 150/300 = 0.50. B delivers more useful joules in these runs, despite having the smaller useful fraction. (b) Complement the useful fraction. The thermal fractions are fA = 80/200 = .40 , fB = 150/300 = .50 . A wastes a smaller fraction of its input, even though B delivers more useful joules. (c) Follow where the energy goes. No. Thermal energy leaves the selected converter and enters its surroundings. Enlarging the system to include the receiving surroundings puts that energy inside the accounting boundary; useful is a task-dependent label.

Question 8

Usable output is not the same as total energy

For this introductory problem use the supplied accounting rule ΔE=Ein−Eout\Delta E=E_{\mathrm{in}}-E_{\mathrm{out}}, with all quantities in joules. Converter A receives 200 J and delivers 120 J to a desired output; 80 J goes to thermal surroundings. Converter B receives 300 J, delivers 150 J to the desired output, and releases 150 J thermally. Neither changes its stored energy. Define the useful fraction as useful output divided by input.

Diagram shown in the original SVG worksheet.

  1. Find each useful fraction and compare useful output amounts.

  2. Which converter wastes a smaller fraction under this definition?

  3. Does the thermal output mean energy has been destroyed? Identify the system for which it is an outgoing transfer.

Question 8 - Solution

Usable output is not the same as total energy

Diagram shown in the original SVG worksheet.

(a) Separate a fraction from an amount.

The governing relation is η=EusefulEinput,fthermal=1−η\boxed{\eta=\frac{E_{\mathrm{useful}}}{E_{\mathrm{input}}},\qquad f_{\mathrm{thermal}}=1-\eta} A has 120/200=0.60;120/200=0.60; B has 150/300=0.50.150/300=0.50. B delivers more useful joules in these runs, despite having the smaller useful fraction.

(b) Complement the useful fraction.

The thermal fractions are fA=80/200=.40,fB=150/300=.50.\boxed{f_A=80/200=.40},\qquad\boxed{f_B=150/300=.50}. A wastes a smaller fraction of its input, even though B delivers more useful joules.

(c) Follow where the energy goes.

No. Thermal energy leaves the selected converter and enters its surroundings. Enlarging the system to include the receiving surroundings puts that energy inside the accounting boundary; useful is a task-dependent label.

← Section questionsChapter contents