Mathematical definition of critical point？(thermodynamics)

In summary, the conversation discusses finding the critical point of a gas described by the Van der Waals equation. The individual is struggling with this step for their statistical mechanics homework and is unsure of the mathematical definition of a critical point. They initially thought the equation given on Wikipedia was inadequate, but later realized it should be sufficient for their problem.
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Homework Statement


If a gas is described by Van der Waals eqn (p+a/v^2)(v-b)=kT, find the critical pint p_c, T_c,and v_c

Homework Equations




The Attempt at a Solution


Actually this is just one intermediate step I got stuck for my stat mech homework, I don't even know the mathematical definition for critical point(I didn't learn quite well in my thermodynamics course), the only relevant equation I found is in wiki http://en.wikipedia.org/wiki/Critical_point_(thermodynamics), but I don't think it is adequate for my problem.
 
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Em.. sorry, I made a silly mistake in my mind, equations given in wiki should be adequate for my problem.
 

What is a critical point in thermodynamics?

A critical point is a specific point in a thermodynamic system where the liquid and gas phases become indistinguishable. At this point, the system experiences a phase transition and the properties of the liquid and gas become the same.

How is a critical point determined mathematically?

A critical point is determined mathematically by setting the derivative of a thermodynamic property (such as temperature, pressure, or volume) with respect to another property to zero. This results in an equation that can be solved to find the critical point.

What are the implications of a critical point in thermodynamics?

A critical point has significant implications in thermodynamics as it marks the maximum temperature and pressure at which a substance can exist as a liquid. Beyond this point, the substance will undergo a phase transition into a gas.

How does the behavior of a substance change at its critical point?

At its critical point, a substance's behavior changes dramatically. Its properties, such as density and heat capacity, become infinite and its behavior becomes highly unpredictable. It is also at this point that a substance's phase transition becomes less dependent on external factors such as pressure and temperature.

Can a critical point be observed in everyday life?

In everyday life, critical points can be observed in the behavior of substances such as water and carbon dioxide. For example, water reaches its critical point at a temperature of 647 K and a pressure of 22.1 MPa, while carbon dioxide reaches its critical point at a temperature of 304.2 K and a pressure of 72.9 atm.

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