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What is the compressibility for a Vanderwall's gas at its Boyle's Temp? What's the approach used?

What is the compressibility for a Vanderwall's gas at its Boyle's Temp?


What's the approach used?

Grade:

2 Answers

vikas askiitian expert
509 Points
10 years ago

TB can be derived from the va n der Waals equation of state for a real gas,

p = [RT/(V(m)-b)]-a/V(m)^2

In order to do that, we express the van der Waals equation as

p = [RT/V(m)]{1/[1-b/V(m)] - a/RTV(m)}

So long as b/Vm < 1, we can expand the first term inside the brackets according to

(1 – x)-1 = 1 + x + x2 + ...

which gives

p = [RT/V(m)]{1 + (b - a/RT)/V(m) + ...}

Obviously the virial coefficient B is given by

B = b - a/RT

At the Boyle Temperature B = 0, and so

T(B) = a/bR = 27T(c)/8

(Tc = 8a/27Rb is the critical temperature of the gas.)

Thus, the Boyle temperature may be found for any gas for which the critical temperature has been determined.

Sushant Mehta
4 Points
10 years ago

So does that mean its 1 for low pressures and greater than 1 for high pressures ?

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