Question

find the coefficient of volume expansion for an ideal gas at constant pressure. ​

Answer 1

$\huge \rm {Answer:-}$

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$\sf \red {We\: know:}$

★For n moles of ideal gas,

$\sf \blue {Ideal\: gas\: equation}$

$\sf \to{\fbox{pv=nRT}}$

$\sf \to{\frac{1}{T}=\frac{nR}{p}}$--------->Equation-1

$\sf \to{pdv=nRdT}$

★Pressure is kept constant,

$\sf \to{∆v=vR∆T}$

$\sf \to{\frac{∆v}{∆T}\:{\frac{1}{v}}}$

★If 'γ ' be the co-efficient of volume expansion,

$\sf \to{γ=\frac{1}{v}\:{\frac{dv}{dT}}}$ ---------->Equation-2

★From Equation-1 and Equation-2

$\sf \to {\frac{dv}{dT}=\frac{nR}{p}}$

$\sf \pink {So,}$

$\sf \to {γ=\frac{nR}{pv}}$

$\sf \implies \green{γ=\frac{1}{T}}$

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$\sf \purple {Therefore,}$

★The coefficient of volume expansion for an ideal gas at constant ppressure ${γ=\frac{1}{T}}$

Answer 2

Answer:

Use the equation of state for an ideal gas and the definition of the average coefficient of volume expansion , in the form β=(1/V)dV/dT to show that the average coefficient of volume expansion for an ideal gas at constant pressure is given by β=1/T where T is the absolute temperature .