Exercises: 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?

Marcos has cold hands and rests them on his sister's mug of hot chocolate. Shortly after, his hands feel much better.

1. a) Have Marcos's hands received energy by work or by heat?
2. b) Which body has given off energy and which has gained it?

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.

Complete the sentence with the missing words: "A system can gain or lose energy in two ways: through $\dots$, when a $\dots$ produces a displacement, or through $\dots$, when there is a $\dots$ difference between two bodies." Then give an everyday example of each way.

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.

When pumping up a bike tyre with a hand pump, the tube of the pump gets hot after a few pumps.

1. a) What work is done in each pump stroke, and on what?
2. b) Explain why the tube gets hot even though there is no heat source nearby.

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.

State whether the sentence is true or false and correct the idea: "When I put an ice cube into a soft drink, the cold from the ice passes into the drink, which is why it cools down."

The work done by a constant force pushing a body in the direction of motion is calculated using $W = F \times d$, where $d$ is the distance travelled. In the supermarket, Noa pushes the trolley with a force of $20\ \text{N}$ over a distance of $5\ \text{m}$ along the aisle, as shown in the figure.

1. a) Calculate the work done.
2. b) What has this work mainly been converted into if the trolley moves faster and faster?

A construction hoist lifts a toolbox by pulling the cable with a force of $250\ \text{N}$ through $6\ \text{m}$ of ascent, as shown in the figure.

1. a) Calculate the work done by the hoist using $W = F \times d$.
2. b) What has happened to the box's energy upon receiving that work?

You want to increase the internal energy of half a liter of tap water and you come up with two plans: put it on the stove in a saucepan or stir it vigorously with a whisk for a long time.

1. a) State by which pathway energy reaches the water in each plan: work or heat.
2. b) Explain what Joule demonstrated with experiments of this type regarding the relationship between work and heat.

A system receives $500\ \text{J}$ of work from its surroundings and, at the same time, transfers $200\ \text{J}$ in the form of heat to the environment, as shown in the figure.

1. a) Calculate by how much the energy of the system has changed.
2. b) Explain what the sign of the result means: does the system end up with more or less energy?

In a warehouse, Leo drags a heavy box across the floor with a constant force of $60\ \text{N}$ over a distance of $12\ \text{m}$, keeping the speed constant throughout, as shown in the figure.

1. a) Calculate the work Leo does on the box.
2. b) If the box does not gain speed, where does that work go? Justify your answer using the first law.

On a building site there are two cranes: crane A lifts a beam by pulling with $400\ \text{N}$ through $3\ \text{m}$ and crane B lifts a bag of cement by pulling with $250\ \text{N}$ through $5\ \text{m}$.

1. a) Calculate the work done by each crane.
2. b) Which of the two has transferred more energy? Comment on whether the crane pulling with greater force is also the one doing the most work.

At the gym, Héctor lifts a weight of $20\ \text{kg}$, which weighs about $200\ \text{N}$ (take $g = 10\ \text{m/s}^2$), from the floor to a height of $1.5\ \text{m}$.

1. a) Calculate the work done in each lift.
2. b) How much total work does he accumulate in a set of $12$ lifts?
3. c) Where does the energy that Héctor transfers to the weight come from?

Cover the outlet of a syringe with your finger and push the plunger with an average force of $40\ \text{N}$; the plunger advances $5\ \text{cm}$, as shown in the figure.

1. a) Express the displacement in meters.
2. b) Calculate the work you do on the trapped air using $W = F \times d$.
3. c) Predict what happens to the temperature of the trapped air and justify your answer.

A car goes down a mountain pass of $8\ \text{km}$ with the brake applied almost all the time. On the descent, the brakes dissipate a total of $400\,000\ \text{J}$ distributed equally among the four discs.

1. a) How much energy does each disc receive, assuming an equal distribution?
2. b) Does that energy reach the discs through work or through heat, and where does it go afterwards?
3. c) Explain why relying too much on the brakes on long descents is dangerous and why engine braking helps, using the idea that energy does not disappear.

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.

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.

The combustion of gasoline 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".

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.

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.

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.