This is the ideal gas from problem 2

In connection to Problem 2, recall that for adiabatic work the system temperature must change and the evaluation of work is done through evaluation of U. We need to know the molar heat capacity at constant volume, which for a monatomic ideal gas is (3/2)R. a. Derive the formula to evaluate the expected temperature change by starting with the first law of thermodynamics, applied to adiabatic change. Replace U with an expressior related to the heat capacity of the system and replace work with the general definition for "PV" work, assuming the ideal EOS. Rearrange using separation of variables and integrate both sides from initial to final conditions. Use this equation to evaluate the final temperature for the adiabatic expansion of the ideal gas in Problem 2 AND calculate the associated work. 2. A monoatomic ideal gas at 300K and 5.00 bar pressure is confined in a piston set at 0.80L. First find the number of moles. Then, calculate the total work released when the gas expands to 2.0L a. against a constant 2.0 bar pressure b. in two steps, first from 0.80L to 1.60L at 2.5 bar pressure then to 2.0L at 2.0 bar pressure. c. Isothermally and reversibly