Question
Determine the ratio ( $\mathrm{p} V / R T)$ at the critical point for a gas which obeys the equation of state (Dieterici's equation)$$p(V-b)=R T \exp (-a / R T V) .$$Give the numerical answer accurately to two significant figures.
Step 1
At the critical point, the first and second derivatives of pressure with respect to volume must be zero. This means we need to find the values of \( p \), \( V \), and \( T \) at the critical point. Show more…
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Show that the critical constants of a substance obeying the Dieterici equation of state, P(v - b) exp (a/vRT) = RT, are Pc = a/4e^2b^2, vc = 2b, Tc = a/4Rb. Compare the ratio Pcvc/RTc for a Dieterici gas with the experimental values in Table 2-4.
Derive the critical constants (Pc, Vc, Tc) of the Dieterici gas obeying the equation of state below with the constants a and b: Hint: 1. Your answers should be expressed in terms of a, b, R, numbers, and constants if necessary. 2. Use the fact that at the critical point, we have these two conditions satisfied below due to the fact that the P-V diagram has an inflection point at the critical point:
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