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**1. Homework Statement**

To a very good approximation, ammonia obeys the Bertholet equation of state,

which reads

PV=nRT+[itex]\frac{9}{128}[/itex]([itex]\frac{nRTc}{Pc}[/itex])(1-6[itex]\frac{Tc^2}{T^2}[/itex])P

a)Suppose we have 500 grams of ammonia under a pressure of P=3.04 atm

and at T=323K. Calculate the volume of ammonia according to the

Bertholet equation of state and compare to the result predicted by the ideal

gas law.

b)Assuming ammonia obeys the Bertholet equation of state obtain

expressions for the coefficient of thermal expansion[itex]\beta[/itex]=[itex]\frac{1}{V}[/itex]([itex]\frac{dV}{dT}[/itex])p and the isothermal compressibility [itex]\kappa[/itex]=[itex]\frac{-1}{V}[/itex]([itex]\frac{dV}{dP}[/itex])T (note: these are partial derivatives at constant P and T). Evaluate β and κ for 500 grams of ammonia at P=3.04 atm and at T=323K.

c)Using your results from part b, calculate ([itex]\frac{dU}{dV}[/itex])T and ([itex]\frac{dH}{dP}[/itex])T for 500 grams of ammonia at P-3.04 atm and T=323K.

**2. Homework Equations**

**3. The Attempt at a Solution**

Ok, so I found the answer to part A which was 0.251 m^3 using Bertholet eqn. of state and 0.256 m^3 using ideal gas law.

Now im not sure about part B. I have a feeling I can accomplish this buy simply solving for volume with Bertholet eqn. of state (or ideal gas law) and simply evaluating the derivative at that point; with T being my variable for beta and P being the variable for kappa. Is that the proper way to evaluate beta and kappa in this situation? Thanks for the help.

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