The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation PT² =constant. The volume expansion coefficient of the gas will be:

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$\frac{3}{T^{3}}$

$\frac{3}{T^{2}}$

$\frac{3}{T}$

$3 T^{2}$

answer is C.

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Detailed Solution

$\begin{array}{l} {PT}^{2} = constant \\ \frac{nRT}{V} T^{2} = constant \\ \Rightarrow V = {KT}^{3} \\ γ = \frac{1}{V} \frac{dv}{dt} = \frac{3}{T} \end{array}$

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