For an ideal gas, the internal energy does not change in any isothermal process since U is only a function of temperature. However, it does change for real gases. As explained in class, the "internal pressure" of a real gas T can be used to calculate the change in its internal energy at constant temperature, UT. Eventually we will prove that the internal pressure of any gas is given by T=T(TP)VP. b) For the van der Waals gas, show that T=a/V2. c) From c), what will the sign of UT be if a van der Waals gas expands isothermally? In other words, will U increase or decrease? Is this result consistent with the KeyesSears experiment? Explain your answer. d) Using the Redlich-Kwong equation of state, derive a formula for T as a function of (n,T,V) ( P should not appear explicitly in your final answer). e) Compare and contrast the two formulas for T. Of the two, which seems the most realistic, and why