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I am learning pure substances in thermodynamics.I read a sentence "Consider a piston cylinder containing liquid at 20 degree celsius and 1 atm pressure."My question is that the pressure of liquid inside the cylinder will increase as we will go downward .So,is 1 atm pressure at the top of the piston or the average pressure of liquid in the piston?

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  • $\begingroup$ As the depth of the liquid can be assumed small, then the pressure given is the dominant term. There is no info about the depth of the liquid so it can be ignored. $\endgroup$
    – Solar Mike
    Jul 4, 2019 at 5:21

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For a gas, the difference is so small it can be ignored.

The density of air at 20C and 1 atm pressure is about 1.2 kg/m^3, so the pressure difference in a 1m tall cylinder is about 1.2 x 9.8 = about 12 Pa. Compare that with the 1 atm pressure which is about 100,000 Pa. The pressure difference is about 0.01% of the total pressure.

Note, this pressure gradient is often not negligible in liquids, where the density is about 1,000 times greater than for gases.

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At any point at the depth of D from the surface of liquid the pressure of liquid is the sum of overbearing one atm pressure and the hydrostatic liquid pressure.

$ P= \rho *g * D + 1atm $

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