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A quarter of a mole of neon gas is in equilibrium at 330 K in a container that has a volume of 5.0L.
(a) How many atoms of neon would you expect to find in one portion of the container that has a volume of 1.0L? Explain your answer in terms of the definition of equilibrium given in our study of entropy.
(b) What is the thermal energy of the gas in this state?
(c) If the container is heated so that the gas reaches a temperature of 380 K, what is the change in the entropy of the system? Assume that the expansion of the container is negligible. (If you can give a number, do so; otherwise, at least say whether the entropy increases or decreases.)
(d) If the expansion of the container is negligible, what must the pressure of the heated gas be?

Respuesta :

Solution :

Given : Volume = 5 L, temperature = 330 K

a).  Moles in one litre,

    [tex]$n_1 =\frac{n}{V}$[/tex]

         [tex]$=\frac{1}{20}$[/tex]

Number of atoms = [tex]$n_1 \times N$[/tex]

                             = [tex]3 \times 10^{22}[/tex]

b). The thermal energy of the gas is :

 [tex]$U=\frac{f}{2} nRT$[/tex]

 U = 10.16 L-atm

c). Given temperature, T = 380 K

  Therefore, Δ S = [tex]\frac{f}{2}nR \ln\left(\frac{T_2}{T_1}\right)[/tex]

                            = 0.004 L-atm/K

d). When the expansion is negligible, the pressure of the heated gas is

   [tex]$P_2=\frac{nRT_2}{V}$[/tex]

       = 1.56 atm

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