At 100. degree C, the constant-volume molar heat capacity of water vapor is 27.5

Question

At 100. degree C, the constant-volume molar heat capacity of water vapor is 27.5 J mol^-1 K^-1; this value rises to 33.1 J mol^-1 K^-1 at 1000. degree C. Based on these experimental values, what types (and how many) of degrees of freedom are contributing to the heat capacity of water vapor at each of these two temperatures? Clearly distinguish which degrees of freedom are fully or partially accessible. Do you expect the specific heat value to increase significantly as the T is raised to 2000. degree C? Briefly explain your answer.

Explanation / Answer

The degrees of freedom is F=C-P+2-r-s

Here,P is the number of phases and C is the number of components, and r is the constant for reaction, and s is the special constant for equilibrium.Here, 2 represents the additional specification temperature and pressure to define the sysytem. As one specification tempertature is given so one specification pressure is needed

At 100 C,

F=1-2+2=1

At 100 C, phase of liquid water and water vapor exists so the phases P is 2.

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At 1000 C,

F=1-1+2=0

At 1000 C, phase of water vapor exists so the phases P is 1.

The degrees of freedom are fully accessible.

The tempertaure effects the Cv value of any substance,

Cv at different temperature is a function of a+bT+cT2+dT5

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