# An Ideal Gas Is Expanding Such That PT2 = Constant.What Is The Coefficient Of Volume Expansion Of The Gas?

PT^{2} \) = constant

\frac{nRT}{V} T^{2} \)= constant

or

T^{3}V^{-1} \)= constant

By Differentiating the equation, we get:

$$\Rightarrow\frac{3T^{2}}{V} * dT – \frac{T^{3}}{V^{2}}dV = 0$$

OR

$$\Rightarrow3dT = \frac{T}{V}*dV$$—[1]

From the equation, dV = VY dT

Where Y = coefficient of volume expansion of gas

$$\Rightarrow\gamma = \frac{1}{V} (\frac{dV}{dT})$$ $$\Rightarrow\gamma = \frac{3}{T}$$

Therefore, the coefficient of volume expansion of the gas is $$\gamma = \frac{3}{T}$$

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