PSRK

Key takeaways

PSRK belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect PSRK to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of PSRK from memory before moving on to harder problems.

Reference excerpt

PSRK (short for Predictive Soave–Redlich–Kwong) is an estimation method for the calculation of phase equilibria of mixtures of chemical components. The original goal for the development of this method was to enable the estimation of properties of mixtures containing supercritical components. This class of substances cannot be predicted with established models, for example UNIFAC.

Principle PSRK is a group-contribution equation of state. This is a class of prediction methods that combines equations of state (mostly cubic) with activity coefficient models based on group contributions, such as UNIFAC. The activity coefficient model is used to adapt the equation-of-state parameters for mixtures by a so-called mixing rule. The use of an equation of state introduces all thermodynamic relations defined for equations of state into the PRSK model. This allows the calculation of densities, enthalpies, heat capacities, and other properties.

Equations As stated previously, the PSRK model is based on a combination of the Soave–Redlich–Kwong equation of state with a mixing rule whose parameters are determined by the UNIFAC method.

Equation of state The equation of state of Soave is defined as follows:

P = R T v − b − a α ( T ) v ( v + b ) . {\displaystyle P={\frac {RT}{v-b}}-{\frac {a\alpha (T)}{v(v+b)}}.}

The original α-function has been replaced by the function of Mathias–Copeman:

α ( T r ) = [ 1 + c 1 ( 1 − T r ) + c 2 ( 1 − T r ) 2 + c 3 ( 1 − T r ) 3 ] 2 . {\displaystyle \alpha (T_{r})=\left[1+c_{1}\left(1-{\sqrt {T_{r}}}\right)+c_{2}\left(1-{\sqrt {T_{r}}}\right)^{2}+c_{3}\left(1-{\sqrt {T_{r}}}\right)^{3}\right]^{2}.}

The parameters of the Mathias–Copeman equation are fitted to experimental vapor-pressure data of pure components and provide a better description of the vapor pressure than the original relation. The form of the equation is chosen as it can be reduced to the original Soave form by setting the parameters c2 and c3 to zero. Additionally, the parameter c1 can be obtained from the acentric factor, using the relation

c 1 = 0.48 + 1.574 ω − 0.176 ω 2 . {\displaystyle c_{1}=0.48+1.574\,\omega -0.176\,\omega ^{2}.}

This may be performed if no fitted Mathias–Copeman parameter is available.

Mixing rule The PSRK mixing rule calculates the parameters a and b of the equation of state by

a b R T = ∑ i x i a i b i R T − g 0 E R T + ∑ x i ln ⁡ b b i 0.64663 {\displaystyle {\frac {a}{bRT}}=\sum _{i}x_{i}{\frac {a_{i}}{b_{i}RT}}-{\frac {{\frac {g_{0}^{E}}{RT}}+\sum x_{i}\ln {\frac {b}{b_{i}}}}{0.64663}}}

and

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with PSRK

Start with the simplest possible case. Write down what PSRK claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to PSRK before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about PSRK ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of PSRK

In research: PSRK appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses PSRK in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: PSRK is common in secondary-school and first-year university syllabi. It links to neighbouring topics Thermodynamic models, so understanding it makes those chapters shorter.
In everyday life: Look for PSRK outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study PSRK in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what PSRK means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain PSRK out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is PSRK in simple terms?

PSRK (short for Predictive Soave–Redlich–Kwong) is an estimation method for the calculation of phase equilibria of mixtures of chemical components. The original goal for the development of this method was to enable the estimation of properties of mixtures containing supercritical components.

Why does PSRK matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study PSRK?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on PSRK.