2. [5 Pts] Prove the followings. Use diagrams if applicable. Explain your statements in detail. (a) Violation of Kelvin-Planck statement implies violation of Clausius statement. [2 Pts] (b) Violation of Clausius statement implies violation of Kelvin-Planck. [2 Pts] (c) You can build an engine with 100% efficiency if you can break the second law. [1 Pt] 3. [8 Pts] A frictionless piston-cylinder connected to a linear spring is filled with saturated liquid ammonia at some temperature (Tsat, Psat). When the piston touches the bottom of the cylinder, the spring is slightly compressed. The spring constant is K, and the cylinder has a uniform cross section A. The system is heated constantly by an external heat source, expanding the ammonia through vaporization, and pushing the piston at a constant speed of x. Express your answers in terms of given parameters. Ammonia (a) If the specific internal energies of ammonia are ug (vapor) and us (liquid) at the beginning, what is the change in internal energy per unit mass of transformed vapor [1-Pt]? (b) If the specific volumes of ammonia are vg (vapor) and vf (liquid) at the beginning, what is the change in specific volume per unit mass of transformed vapor x [1 Pt]? (c) What is the change in the internal energy per volume change? [1 Pt] (Hint: the final unit should be J/m or kJ/m) (d) What is the change in the volume per change in internal energy? [1 Pt] (e) What is the rate of change in the internal energy in kJ/s? [1 Pt] (f) What is the working power of ammonia? [1 Pt] (g) What is the heating power from the external heat source? [2 Pts]