When an ideal gas is compressed at constant temperature (isothermal conditions), E is zero. Consider 9.00 L

When an ideal gas is compressed at constant temperature (isothermal conditions), ΔE is zero. Consider 9.00 L of a gas that is initially at 1.00 atm and 25 °C.

(a) Calculate q and w if the gas sample is compressed isothermally at a constant pressure of 9.00 atm to a fi nal volume of 1.00 L.

(b) Calculate q and w if the gas is compressed isothermally in two steps: first at a constant pressure of 3.00 atm (to an intermediate volume of 3.00 L) and then at a pressure of 9.00 atm (and a final volume of 1.00 L).

(c) Calculate q and w of a three-step isothermal compression (first to 2.00 atm and 4.50 L, then to 3.00 atm and 3.00 L, and finally 9.00 atm and 1.00 L). Compare with the two- and one-step compressions.

(d) Based on your results for parts a to c, suggest how this compression might be carried out so that the minimum amount of work would be done on the system.