Question

Calculate the specific volume of normal butane at a pressure of 80 bar and a temperature of 227° C is desirable as follows:

1, the ideal gas equation

2, the compressibility coefficient of the Peters method

3, virial equations up to a factor of two

4, Redlish Quang equation

Answer 1

1. The ideal gas equation:

$$pV=\dfrac mMRT→v=\dfrac Vm=\dfrac{RT}{pM},\\\space\\ v=8.84·10^{-3}\text{ m}^2/\text{kg}.$$

2. The compressibility factor:

$$z=\dfrac{pV}{nRT}=0.99973.$$

The specific volume:

$$v_P=zv=8.838·10^{-3}\text{ m}^2/\text{kg}.$$

3. Virial equations up to a factor of two:

$$Z\equiv\dfrac{Pv}{RT}=17.23.$$

4. The coefficients for Redlish-Quang equation (the critical pressure for butane is 3.796 MPa, critical temperature for butane is 425.1 K):

$$a=0.42748\dfrac{R^2T_c^{2.5}}{P_c}=29.0059,\\\space\\ b=0.08664\dfrac{RT_c}{P_c}=29.0059=8.067·10^{-5}.$$