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Chapter 17: Problem 2

According to the ideal-gas law, what should be the volume of a gas at absolute zero? Why is this result absurd?

Short Answer

Expert verified
According to the ideal-gas law, the volume of a gas at absolute zero should theoretically be zero. This result is absurd because it contradicts the physical reality that gas particles do occupy space, and therefore, cannot have a zero volume.

Step by step solution

01

Understanding the Ideal Gas Law

The ideal gas law is represented by the formula \(PV=nRT\), where:\(P\) = pressure of the gas,\(V\) = volume of the gas,\(n\) = number of moles of the gas,\(R\) = ideal gas constant, and \(T\) = absolute temperature (in Kelvin).
02

Substituting the given temperature

In this case, the absolute temperature (\(T\)) is given as absolute zero, which is \(0\) Kelvin. If we substitute this value in the ideal gas law formula, we get: \(PV=nR*0\).
03

Simplifying the equation

By multiplying, we get: \(PV=0\). Since \(P\), \(n\) and \(R\) are not zero, for the equation to hold, \(V\) must be zero. Therefore, according to the ideal gas law, the volume of the gas at absolute zero should be zero.
04

Absurdity of the Result

This result is absurd because it contradicts the physical reality of gases. The volume of a gas cannot actually be zero as it would imply that the gas is non-existent or its particles occupy no space which is impossible.

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Most popular questions from this chapter

The average speed of the molecules in a gas increases with increasing temperature. What about the average velocity?

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