# what is P-V isotherm?

A graph between P and V of a fixed amount of gas at constant temperature is called p-v Isotherm.

• Graphical representation of constant temperature

• Each line is called isotherm (at constant temperature plot).

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For an isothermal, reversible process, this integral equals the area under the relevant pressure-volume isotherm, and is indicated in blue in the figure (at the bottom right-hand of the page) for an ideal gas. Again, p = nRT / V applies and withT being constant (as this is an isothermal process), we have:

$W_{Ato B} = int_{V_A}^{V_B}p,dV = int_{V_A}^{V_B}frac{nRT}{V}dV = nRTint_{V_A}^{V_B}frac{1}{V}dV = nRTln{frac{V_B}{V_A}}$

Hope it helps U :)
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thank u!

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