Is the potential energy on the surface of Earth zero?If not, what will be it's value?

Potential energy does not have an absolute measurement. It is always relative to some reference point. Gravitational potential always increases when you go up and decreases when you go down. But the choice of a zero point is arbitrary.

If you’re dropping objects onto the ground, then choosing the ground as a zero point makes the calculations easier. But you could just as easily make the zero point the top of Mt. Everest, and all the answers would turn out the same. Up still means more energy and down means less, but now the PE of an object at sea level would have a negative sign, but not as negative as an object ten meters above sea level.

So everything would still work fine.

In fact, planetary astronomers take this idea to extremes. Instead of the top of Mt. Everest, they set the zero point for potential energy as infinitely high—so far “up” that gravity is so weak that going “up” another kilometer doesn’t gain you any energy. Then the value for potential energy everywhere else in the universe anywhere near a planet has a negative sign, but just as before, all the answers in relative terms turn out fine.

Explanation:

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heat the gas and measure the pressure