Work and heat as energy transfers

Irene goes down a long hill on her bike and squeezes the brake almost all the time. On reaching the bottom, she carefully touches the brake pad and notices that it is hot.

1. a) Has the energy reached the brake pad through work or through heat?
2. b) What force carried out this energy transfer?

Classify each situation according to whether energy is transferred by work (a force acts) or by heat (there is a temperature difference):

1. a) You stretch a rubber band with your fingers.
2. b) A cold frying pan on an electric ceramic hob that is switched on.
3. c) The blender stirs the juice forcefully.
4. d) You warm your hands by putting them near a campfire.
5. e) You rub your hands together to warm up.

In the International System of Units, both work and heat are measured in joules ($\text{J}$), the same unit as energy. Explain in your own words why it makes sense for all three to share the same unit.

In a classic experiment such as Joule's, a weight of $4\ \text{kg}$ falls and turns paddles that stir the water in a container, as shown in the figure. Take $g = 10\ \text{m/s}^2$, so that the weight pulls the string with a force of $40\ \text{N}$.

1. a) If the weight descends $1,5\ \text{m}$, calculate the work it does on the paddles in one fall.
2. b) The weight is lifted and released again $25$ times. How much total work has been transferred to the water?
3. c) What has that work been converted into inside the container? Explain what equivalence between work and heat this experiment illustrates.

A car travelling at $90\ \text{km/h}$ brakes to a complete stop. Has the energy carried by the car disappeared? Explain where it has gone according to the first law of thermodynamics.

A motor pulls a box along a rough floor at constant speed, doing $1000\ \text{J}$ of work. Along that same path, friction with the floor dissipates $1000\ \text{J}$ in the form of heat, as shown in the figure.

1. a) By how much has the box's energy increased in that section?
2. b) Relate the previous result to the fact that the speed is constant.
3. c) If the motor had done $1300\ \text{J}$ of work in the same section, what would have happened to the box? Quantify it.

The combustion of petrol in a tank releases $20\,000\ \text{J}$ of chemical energy. Of this, the car's wheels receive $6000\ \text{J}$ of useful work, as shown in the figure.

1. a) Calculate how much energy is lost in the form of heat.
2. b) What percentage of the fuel energy is used as work?
3. c) State where heat leaves the car and explain why this energy balance does not contradict the first law, even though energy is "lost".

During a certain interval, the solar panels of the International Space Station capture $100\,000\ \text{J}$ of solar energy. Of this, $40\,000\ \text{J}$ power the onboard electronics and $35\,000\ \text{J}$ are stored in the batteries.

1. a) Calculate how much energy is dissipated as heat.
2. b) Classify each of the three destinations according to whether it is a transfer by work, by heat, or energy storage.
3. c) Explain in your own words what the first law of thermodynamics states, using this balance as an example.

In a forge, the blacksmith strikes a piece of red-hot iron, and each hammer blow transfers a work of $150\ \text{J}$ to it. In total he strikes $40$ blows.

1. a) Calculate the total work transferred to the iron.
2. b) When finished, the internal energy of the iron has only increased by $3000\ \text{J}$. What has happened to the rest of the energy?
3. c) Explain using the first law why the blacksmith hears the blow and feels heat on his face at the same time.

When inflating a tyre with a hand pump, with each stroke you push the piston with an average force of $60\ \text{N}$ over a distance of $0,3\ \text{m}$.

1. a) Calculate the work of each stroke and that of $50$ consecutive strokes.
2. b) If of the total only $600\ \text{J}$ goes into increasing the energy of the air and the hose, how much energy has been transferred to the surroundings and in what form?
3. c) Explain why the pump hose is warm when finished even though you have not brought it near any heat source.

Two inventors present their machines. Inventor A claims that his machine receives $600\ \text{J}$ of energy from a fuel and delivers $1000\ \text{J}$ of work. Inventor B claims that his receives $1000\ \text{J}$ and delivers $700\ \text{J}$ of work, releasing another $300\ \text{J}$ as heat. The energy balances of each machine are shown in the figure.

1. a) Evaluate Inventor A's machine using the first law: is it possible? Reason your answer using the energy balance.
2. b) Do the same for Inventor B's machine.
3. c) State the first law of thermodynamics in your own words.