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When we drive a car, we use gasoline as the source of energy. When we arrive at the destination, we lose some of the gasoline, used to move the car from one point to another. Then how energy is conserved, if we spend energy to move the car?

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    $\begingroup$ Conservation of energy does not mean you can drive or heat your house for free. $\endgroup$ – Alchimista Jan 26 '18 at 9:09
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What does it mean to "spend energy"? In the concrete example, the engine converts the chemical energy in the gasoline through combustion into kinetic energy of the car.

While the car is moving, it feels friction with the surface and air, so some of the kinetic energy of the car goes into friction (heat, air movement, etc).

When you stop the car, the kinetic energy completely goes into friction in the brakes, asphalt and air (again, as heat or kinetic energy of the air molecules, etc).

Conservation of energy means that in a closed system the energy stays constant. If you look just at the car and not also at the surroundings, that is not a closed system, and that principle is not applicable here. However, you can look at the surroundings too; then it all works out.

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How does the car loose that energy, when we stop the car again after our trip?

The answer is brakes.

(And maybe also a potential energy increase as well as friction as well as air resistance etc...)

When you brake, the brake shoes are pressed onto the brake drum (or brake pads onto brake discs or similar for other braking systems). This causes large amounts of friction. That releases heat (the drum gets very, very varm after long-term or hard braking).

This is where the energy goes! It is converted into heat and disappears into the surrounding air.

Energy conservation is valid since the chemical energy ends up as thermal energy leaving the car as heat. No energy is disappearing from this world, no energy is created out of the blue - one energy form is just converted into some other energy form.

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