t differential The first and second laws of thermodynamics can be combined to generate an exac equation of internal energy change (): 1. Using this equation, derive exact differentials of H. A and G 2ã The following image shows Ca adiabatic expansion and isothermal expansion, prove that this cycle entropy. ( ds-0) e shows Carnot cycle beginning from the point A and resuns back to A. Using rnot cyci (1 â 4) has no net change in The following equation shows Maxwell relation of Helmholtz energy exact differential equation. 3. os Lar/v aV/T (a) Derive this Maxwell relation from the given exact differential equation (b) (extra credit) Using the Maxwell relation above, derive the following equation ãããã§Â· KaT/y )T ë° is internal pressure, Ï,- From the exact differential of internal energy (U) 4. Suppose that 10.0 mmol of He(g) occupies 90.0 mL at 298 K and expands isothermally to 150.0 ml Calculate Gibbs free energy change (4G) for this expansion