$4\mathrm{.}9.$ Gyro Gearloose, one of our less responsibie students, neglected to close tightly a valve

on his compressed air bottle last Friday. Over the weekend, the bottle pressure dropped

slowly to $)$ bar. Henrietta Helmholtz, his laboratory partner, berated him for his

thoughtlessness. She pointed out that his action had resulted in a serious loss of available

energy.

Her concern was real as it was $-10C$ outside. She insisted that if the bottle had had to be

blown down, she could have devised a more efficient method to provide considerable

energy to heat the laboratory. As she was a first$-$year student, she had not had the

opportunity to benefit from our thorough thermodynamics program and thus was unable

to express her feelings in a quantitarive manner. Could you come to her assistance and

indicate the maximum number of joules that could have been made available for heating

if the bottle had been blown down in a less thoughtless manner? $($Assume ideal gases.$)$

Data:

$($Note: The depariment is well$-$stocked with various sizes of Carnot engines, if needed.$)$

Be certain that you use your most perceptive imagination to work this problem. The bottie

initially is at $20C.$ You may carry out the blowdown process inside or outside the

iaboratory, and you may employ any type of compressor, expander, and heat exchanger

you desire. Neglect, however, the heat capacity of the bottle itself.