Please do all parts of the question below:

An ideal gas undergoes a quasistatic, reversible process. Heat is add/removed to the gas in such a way that at every instant, the pressure and volume are related by P = P0bV , where P0 and b are positive constants.

(a) What are the standard metric (SI) units of b? Explain your answer.

(b) Sketch this process in the P-V plane. Assume the pressure initially starts at P0 at a very small (almost zero) volume, and ends up at a very low (almost zero) pressure. Clearly label the points at which your curve crosses each axis.

(c) What is the largest temperature reached by the gas during this process? Give your answer in terms of constant P0, b, nm, and other known constants and explain how you got it. [Hint: Use calculus to find the maximum of a function.]

(d) Plot the point where the largest temperature occurs on your P-V diagram. Also sketch the isothermal line corresponding to this temperature.

(e) As a concrete example: Suppose that 3 moles of ideal gas starts at an initial Pressure of 4.0atm, and initial temperature of 80K. The gas undergoes the process given in the problem statement and ends up in a final state of pressure 0.5 atm and a final temperature of 80K. What is the numerical value of the hottest temperature reached by the gas during this process?