State the law of conservation of energy.

Energy increases whenever work is done on a system Energy cannot be created or destroyed — it can only be transferred from one form to another, and the total energy of an isolated system remains constant The total energy in the universe decreases slowly over time Energy is conserved only in frictionless systems

A pendulum swings back and forth but gradually slows down. Does this violate conservation of energy?

Yes — the pendulum loses energy, so energy is not conserved in real systems Yes — gravity removes energy from the pendulum each time it swings No — energy is converted to thermal energy by air resistance and friction at the pivot; the total energy including heat is still conserved No — a pendulum never actually slows down; it just appears to from the outside

What is the efficiency of an energy conversion, and how is it expressed?

Efficiency = total energy output ÷ energy lost as heat Efficiency = power input × time taken Efficiency = (useful energy output ÷ total energy input) × 100% — the fraction of input energy that does useful work Efficiency = the number of joules saved compared to an older machine

A car engine is about 25–35% efficient. Where does the other 65–75% of the fuel's chemical energy go?

It is stored in the car battery for later use It is destroyed by friction inside the engine It escapes as radio waves through the exhaust pipe Mostly as thermal energy — heat in the exhaust gases, engine cooling system, and friction between moving parts

Why is it impossible to build a perpetual motion machine — a device that runs forever without any energy input?

Perpetual motion machines are theoretically possible but too expensive to build Every real energy conversion produces some thermal energy that disperses and cannot be fully recovered — so useful energy always decreases, and the machine must eventually stop Gravity would slow down any machine over time Air resistance is always too strong for any machine to overcome

At the top of a roller coaster's highest point, a car is moving slowly. At the bottom of the same drop it is moving very fast. Which statement correctly describes the energy transformation?

Kinetic energy at the top is converted into gravitational potential energy at the bottom The motor at the top of the drop transfers electrical energy to the car Gravitational potential energy at the top is converted into kinetic energy at the bottom — with a small amount converted to thermal energy by friction and air resistance Chemical energy in the passengers is converted into kinetic energy

In 1824, the French engineer Sadi Carnot proved that even a theoretically perfect heat engine cannot be 100% efficient. What deep reason explains this?

Friction in the pistons always wastes some energy as sound No fuel burns completely, so some chemical energy is always wasted Some heat must always flow from the hot reservoir to the cold reservoir without being converted to work — this is required by the Second Law of Thermodynamics Metal expands at high temperatures, reducing the engine's efficiency

You charge your phone overnight. By morning, the battery is full — but you spent the whole night asleep without using it. The next evening the battery is dead. Where did all the stored energy go?

The energy was destroyed when the battery ran out The energy leaked back into the power grid through the charger port It was converted to light (screen), sound, radio waves (Wi-Fi, cellular), and ultimately thermal energy that dissipated into the surroundings The energy was stored as heat in the phone's case and then lost during the night

James Prescott Joule's famous paddle-wheel experiment stirred water using a falling weight and measured the temperature rise. What was the revolutionary conclusion?

Water heats up when stirred because stirring adds mass to the water Mechanical work and heat are equivalent forms of the same thing — energy — and can be converted into each other at a fixed rate Falling weights lose all their potential energy to sound when they hit the ground Water stores potential energy when it is stirred in a circular motion

In any ecosystem, there are far more plants than herbivores, and far more herbivores than carnivores. How does the law of conservation of energy explain this pattern?

Carnivores eat faster, so they need fewer members to consume the same energy Plants are smaller than animals, so they need more individuals to fill the same space Only about 10% of the energy at each level passes to the next — the rest is lost as heat; so each higher level in the food chain has less energy available to support organisms Carnivores choose not to breed as much because their food sources are unreliable