# coefficient of volume expansion of ideal gas

#### ling233

why the coefficient of volume expansion of ideal gas is given by the formula = 1/T ? by saying it = 1/T , the assume delV / V amd delP / P = constant ?
why ? when the temp change , the density and specific volume(v) also change , right ?

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#### ChipB

PHF Helper
Given the Ideal Gas Law rho = P/RT, take the derivative of rho with respect to T:

d rho/dT = -P/(RT^2)

The definition of beta is:

beta = -(1/rho)(d rho/dT) at constant P

So:

beta = -(RT/P)(-P/(RT^2)) = 1/T at constant P.

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