1. The so-called ideal gases are the gases and vapors that follow PV = nRT or on a molar basis PV RT. Considering a closed ideal gas system, = (a) provide proper expressions for (i) pressure change AP under a fixed volume and (ii) volume change AV under a fixed pressure, for the system as functions of temperature change AT. (b) start from PdV+VdP=RdT to obtain an expression for 1 av T and evaluate its value in SI unit for an ideal gas at 127 °C and 1.25 atm. (c) continue from (a) and (b) to show that ideal gases also satisfy aP av эт =-1. av T 2. Three gaseous streams all controlled at 100°C and 2 atm deliver 250 moles/min of water, 350 moles/min of methanol, and 400 moles/min of ethanol into a unit to form a mixture. Calculate (a) the average molecule weight of the mixture (b) the mass fractions and then the average molecule weight (c) the volumetric flow rates of the three process streams in m³/min using the ideal gas law. Please refer to Table B. 1 for molecular masses/weights. 3. At a place where the atmospheric pressure is 100 kPa. a 5-kg piston sits near the bottom of a vertically placed cylinder that contains a negligible amount of gas. The piston is 100 mm in diameter and is loaded with a spring which exerts no force on the piston initially. After a small valve is opened to let some gas in slowly from a high pressure source, the pressure and volume of the cylinder are measured to be 400 kPa and 0.4 L, respectively. If the valve is opened again in order to bring the piston up another 2 cm, estimate (a) the initial pressure of the cylinder (b) the force from the spring on the piston when the pressure is 400 kPa AP (c) the final pressure. You may consider constant for this problem. AV 4. A cylinder-piston system contains 3 mole of an ideal gas at 127 °C. If the system is compressed isothermally and very slowly by the piston so that the work can be expressed as dW --PdV calculate the amount of work required to have the volume halved. Should this work be >0 or <0? Please explain.